Mathematics Homework Help

A random sample of 51 adult coyotes in a region of northern Minnesota showed the average age to be x = 2.05 years, with sample standard deviation s = 0.88 years. However, it is thought that the overall population mean age of coyotes is μ = 1.75. Do the sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years? Use α = 0.01.(a) What is the level of significance?

State the null and alternate hypotheses.H₀: μ = 1.75 yr; H₁: μ < 1.75 yrH₀: μ = 1.75 yr; H₁: μ ≠ 1.75 yr H₀: μ < 1.75 yr; H₁: μ = 1.75 yrH₀: μ > 1.75 yr; H₁: μ = 1.75 yrH₀: μ = 1.75 yr; H₁: μ > 1.75 yr

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The Student’s t, since the sample size is large and σ is unknown.The standard normal, since the sample size is large and σ is known. The standard normal, since the sample size is large and σ is unknown.The Student’s t, since the sample size is large and σ is known.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

(c) Find the P-value. (Round your answer to four decimal places.)

Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.01 level to conclude that coyotes in the specified region tend to live longer than 1.75 years.There is insufficient evidence at the 0.01 level to conclude that coyotes in the specified region tend to live longer than 1.75 years.

10.–/8 pointsBBUnderStat11 8.2.014.Ask Your Teacher

My Notes

Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for cutthroat trout. Suppose a friend tells you that the average length of trout caught in Pyramid Lake is μ = 19 inches. However, a survey reported that of a random sample of 46 fish caught, the mean length was x = 18.7 inches, with estimated standard deviation s = 3.4 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than μ = 19 inches? Use α = 0.05.(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: μ = 19 in; H₁: μ > 19 inH₀: μ < 19 in; H₁: μ = 19 in H₀: μ = 19 in; H₁: μ < 19 inH₀: μ = 19 in; H₁: μ ≠ 19 inH₀: μ > 19 in; H₁: μ = 19 in
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The Student’s t, since the sample size is large and σ is unknown.The standard normal, since the sample size is large and σ is known. The Student’s t, since the sample size is large and σ is known.The standard normal, since the sample size is large and σ is unknown.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

(c) Find the P-value. (Round your answer to four decimal places.)

Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.05 level to conclude that the average fish length is less than 19 inches.There is insufficient evidence at the 0.05 level to conclude that the average fish length is less than 19 inches.

11.–/8 pointsBBUnderStat11 8.2.015.Ask Your Teacher

My Notes

Socially conscious investors screen out stocks of alcohol and tobacco makers, firms with poor environmental records, and companies with poor labor practices. Some examples of “good,” socially conscious companies are Johnson and Johnson, Dell Computers, Bank of America, and Home Depot. The question is, are such stocks overpriced? One measure of value is the P/E, or price-to-earnings ratio. High P/E ratios may indicate a stock is overpriced. For the S&P Stock Index of all major stocks, the mean P/E ratio is μ = 19.4. A random sample of 41 “socially conscious” stocks gave a P/E ratio sample mean of x = 18.4, with sample standard deviation s = 5.8. Does this indicate that the mean P/E ratio of all socially conscious stocks is different (either way) from the mean P/E ratio of the S&P Stock Index? Use α = 0.01.(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: μ ≠ 19.4; H₁: μ = 19.4H₀: μ = 19.4; H₁: μ > 19.4 H₀: μ = 19.4; H₁: μ ≠ 19.4H₀: μ = 19.4; H₁: μ < 19.4H₀: μ > 19.4; H₁: μ = 19.4
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The Student’s t, since the sample size is large and σ is unknown.The standard normal, since the sample size is large and σ is known. The standard normal, since the sample size is large and σ is unknown.The Student’s t, since the sample size is large and σ is known.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

(c) Find the P-value. (Round your answer to four decimal places.)

Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.01 level to conclude that the mean P/E ratio of all socially conscious stocks differs from the mean P/E ratio of the S&P Stock Index.There is insufficient evidence at the 0.01 level to conclude that the mean P/E ratio of all socially conscious stocks differs from the mean P/E ratio of the S&P Stock Index.

12.–/8 pointsBBUnderStat11 8.2.016.Ask Your Teacher

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Unfortunately, arsenic occurs naturally in some ground water†. A mean arsenic level of μ = 8.0 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 36 tests gave a sample mean of x = 7.2 ppb arsenic, with s = 2.6 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use α = 0.10.(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: μ < 8 ppb; H₁: μ = 8 ppbH₀: μ > 8 ppb; H₁: μ = 8 ppb H₀: μ = 8 ppb; H₁: μ < 8 ppbH₀: μ = 8 ppb; H₁: μ ≠ 8 ppbH₀: μ = 8 ppb; H₁: μ > 8 ppb
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The standard normal, since the sample size is large and σ is known.The Student’s t, since the sample size is large and σ is known. The Student’s t, since the sample size is large and σ is unknown.The standard normal, since the sample size is large and σ is unknown.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

(c) Find the P-value. (Round your answer to four decimal places.)

Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.10 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.10 level to conclude that the mean level of arsenic in the well is less than 8 ppb.There is insufficient evidence at the 0.10 level to conclude that the mean level of arsenic in the well is less than 8 ppb.

13.–/10 pointsBBUnderStat11 8.2.017.Ask Your Teacher

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Let x be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal. For the population of healthy female adults, suppose the mean of the x distribution is about 4.64. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient’s doctor are as follows.

4.9

4.2

4.5

4.1

4.4

4.3

(i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)

x	=
s	=

(ii) Do the given data indicate that the population mean RBC count for this patient is lower than 4.64? Use α = 0.05.

(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: μ > 4.64; H₁: μ = 4.64H₀: μ = 4.64; H₁: μ ≠ 4.64 H₀: μ = 4.64; H₁: μ > 4.64H₀: μ < 4.64; H₁: μ = 4.64H₀: μ = 4.64; H₁: μ < 4.64
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The Student’s t, since we assume that x has a normal distribution and σ is known.The standard normal, since we assume that x has a normal distribution and σ is known. The standard normal, since we assume that x has a normal distribution and σ is unknown.The Student’s t, since we assume that x has a normal distribution and σ is unknown.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

(c) Find the P-value. (Round your answer to four decimal places.)

Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.05 level to conclude that the population mean RBC count for the patient is lower than 4.64.There is insufficient evidence at the 0.05 level to conclude that the population mean RBC count for the patient is lower than 4.64.

14.–/10 pointsBBUnderStat11 8.2.018.Ask Your Teacher

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Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of whole blood. Then x has a distribution that is approximately normal, with population mean of about 14 for healthy adult women. Suppose that a female patient has taken 10 laboratory blood tests during the past year. The HC data sent to the patient’s doctor are as follows.

16

18

16

20

14

12

15

17

17

11

(i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)

x	=
s	=

(ii) Does this information indicate that the population average HC for this patient is higher than 14? Use α = 0.01.

(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: μ = 14; H₁: μ ≠ 14H₀: μ = 14; H₁: μ < 14 H₀: μ > 14; H₁: μ = 14H₀: μ = 14; H₁: μ > 14H₀: μ < 14; H₁: μ = 14
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The standard normal, since we assume that x has a normal distribution and σ is unknown.The Student’s t, since we assume that x has a normal distribution and σ is known. The standard normal, since we assume that x has a normal distribution and σ is known.The Student’s t, since we assume that x has a normal distribution and σ is unknown.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

(c) Find the P-value. (Round your answer to four decimal places.)

Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.01 level to conclude that the population average HC for this patient is higher than 14.There is insufficient evidence at the 0.01 level to conclude that the population average HC for this patient is higher than 14.

15.–/10 pointsBBUnderStat11 8.2.019.Ask Your Teacher

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Snow avalanches can be a real problem for travelers in the western United States and Canada. A very common type of avalanche is called the slab avalanche. These have been studied extensively by David McClung, a professor of civil engineering at the University of British Columbia. Suppose slab avalanches studied in a region of Canada had an average thickness of μ = 67 cm. The ski patrol at Vail, Colorado, is studying slab avalanches in its region. A random sample of avalanches in spring gave the following thicknesses (in cm).

59	51	76	38	65	54	49	62
68	55	64	67	63	74	65	79

(i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)

x	=	cm
s	=	cm

(ii) Assume the slab thickness has an approximately normal distribution. Use a 1% level of significance to test the claim that the mean slab thickness in the Vail region is different from that in the region of Canada.

(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: μ = 67; H₁: μ ≠ 67H₀: μ = 67; H₁: μ > 67 H₀: μ < 67; H₁: μ = 67H₀: μ ≠ 67; H₁: μ = 67H₀: μ = 67; H₁: μ < 67
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The Student’s t, since we assume that x has a normal distribution and σ is known.The Student’s t, since we assume that x has a normal distribution and σ is unknown. The standard normal, since we assume that x has a normal distribution and σ is unknown.The standard normal, since we assume that x has a normal distribution and σ is known.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

(c) Find the P-value. (Round your answer to four decimal places.)

Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.01 level to conclude that the mean slab thickness in the Vail region is different from that in the region of Canada.There is insufficient evidence at the 0.01 level to conlcude that the mean slab thickness in the Vail region is different from that in the region of Canada.

16.–/10 pointsBBUnderStat11 8.2.020.Ask Your Teacher

My Notes

A national newspaper reported that the state with the longest mean life span is Hawaii, where the population mean life span is 81 years. A random sample of 20 obituary notices in the Honolulu Advertizer gave the following information about life span (in years) of Honolulu residents.

72	68	81	93	56	19	78	94	83	84
77	69	85	97	75	71	86	47	66	27

(i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)

x	=	yr
s	=	yr

(ii) Assuming that life span in Honolulu is approximately normally distributed, does this information indicate that the population mean life span for Honolulu residents is less than 81 years? Use a 1% level of significance.

(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: μ = 81 yr; H₁: μ < 81 yrH₀: μ > 81 yr; H₁: μ = 81 yr H₀: μ = 81 yr; H₁: μ ≠ 81 yrH₀: μ = 81 yr; H₁: μ > 81 yrH₀: μ < 81 yr; H₁: μ = 81 yr
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The Student’s t, since we assume that x has a normal distribution and σ is known.The standard normal, since we assume that x has a normal distribution and σ is known. The standard normal, since we assume that x has a normal distribution and σ is unknown.The Student’s t, since we assume that x has a normal distribution and σ is unknown.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

(c) Find the P-value. (Round your answer to four decimal places.)

Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.01 level to conlcude that the population mean life span of Honolulu residents is less than 81 years.There is insufficient evidence at the 0.01 level to conclude that the population mean life span of Honolulu residents is less than 81 years.

17.–/10 pointsBBUnderStat11 8.2.021.Ask Your Teacher

My Notes

Homser Lake, Oregon, has an Atlantic salmon catch-and-release program that has been very successful. The average fisherman’s catch has been μ = 9.8 Atlantic salmon per day. Suppose that a new quota system restricting the number of fishermen has been put into effect this season. A random sample of fishermen gave the following catches per day:

12	6	11	12	5	0	2
7	8	7	6	3	12	12

(i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)

x	=	catches
s	=	catches

(ii) Assuming the catch per day has an approximately normal distribution, use a 1% level of significance to test the claim that the population average catch per day is now different from 9.8.

(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: μ = 9.8; H₁: μ ≠ 9.8H₀: μ ≠ 9.8; H₁: μ = 9.8 H₀: μ = 9.8; H₁: μ < 9.8H₀: μ = 9.8; H₁: μ > 9.8H₀: μ < 9.8; H₁: μ = 9.8
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The standard normal, since we assume that x has a normal distribution and σ is known.The standard normal, since we assume that x has a normal distribution and σ is unknown. The Student’s t, since we assume that x has a normal distribution and σ is known.The Student’s t, since we assume that x has a normal distribution and σ is unknown.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

(c) Find the P-value. (Round your answer to four decimal places.)

Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.01 level to conclude that the population average catch per day differs from 9.8.There is insufficient evidence at the 0.01 level to conclude that the population average catch per day differs from 9.8.

18.–/10 pointsBBUnderStat11 8.2.022.Ask Your Teacher

My Notes

Tree-ring dating from archaeological excavation sites is used in conjunction with other chronologic evidence to estimate occupation dates of prehistoric Indian ruins in the southwestern United States. Suppose it is thought that a certain pueblo was occupied around 1286 A.D. (based on evidence from potsherds and stone tools). The following data give tree-ring dates (A.D.) from adjacent archaeological sites:

1189

1267

1268

1275

1275

1271

1272

1316

1317

1230

(i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to one decimal place.)

x	=	A.D.
s	=	yr

(ii) Assuming the tree-ring dates in this excavation area follow a distribution that is approximately normal, does this information indicate that the population mean of tree-ring dates in the area is different from (either higher or lower than) 1286 A.D.? Use a 1% level of significance.

(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: μ = 1286; H₁: μ ≠ 1286H₀: μ ≠ 1286; H₁: μ = 1286 H₀: μ > 1286; H₁: μ = 1286H₀: μ = 1286; H₁: μ > 1286H₀: μ = 1286; H₁: μ < 1286
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The standard normal, since we assume that x has a normal distribution and σ is known.The Student’s t, since we assume that x has a normal distribution and σ is unknown. The standard normal, since we assume that x has a normal distribution and σ is unknown.The Student’s t, since we assume that x has a normal distribution and σ is known.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

(c) Find the P-value. (Round your answer to four decimal places.)

Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.01 level to conclude that the population mean of tree-ring dates in the area differs from 1286 A.D.There is insufficient evidence at the 0.01 level to conclude that the population mean of tree-ring dates in the area differs from 1286 A.D.

19.–/4 pointsBBUnderStat11 8.2.023.Ask Your Teacher

My Notes

Consider the following.(a) For the same data and null hypothesis, is the P-value of a one-tailed test (right or left) larger or smaller than that of a two-tailed test? Explain your answer.The P-value for a one-tailed test is larger because the two-tailed test includes the area in both tails.The P-value for a one-tailed test is larger because the two-tailed test includes the area in only one tail. The P-value for a one-tailed test is smaller because the two-tailed test includes the area in only one tail.The P-value for a one-tailed test is smaller because the two-tailed test includes the area in both tails.

(b) For the same data, null hypothesis, and level of significance, is it possible that a one-tailed test results in the conclusion to reject H₀ while a two-tailed test results in the conclusion to fail to reject H₀? Explain your answer.

Yes. The P-value for a one-tailed test might be smaller than α, while the P-value for a two-tailed test could be larger than α.Yes. When the P-value for a one-tailed test is smaller than α, the P-value for a two-tailed test will also be smaller than α. No. When the P-value for a one-tailed test is smaller than α, the P-value for a two-tailed test will also be smaller than α.No. The P-value for a one-tailed test might be smaller than α, while the P-value for a two-tailed test could be larger than α.

(c) For the same data, null hypothesis, and level of significance, if the conclusion is to reject H₀ based on a two-tailed test, do you also reject H₀ based on a one-tailed test? Explain your answer.

No. If the two-tailed P-value is smaller than α, the one-tailed area will be larger than α.No. If the two-tailed P-value is smaller than α, the one-tailed area is also smaller than α. Yes. If the two-tailed P-value is smaller than α, the one-tailed area is also smaller than α.Yes. If the two-tailed P-value is smaller than α, the one-tailed area will be larger than α.

(d) If a report states that certain data were used to reject a given hypothesis, would it be a good idea to know what type of test (one-tailed or two-tailed) was used? Explain your answer.

Yes. The conclusions can be different.No. The conclusions can be different. Yes. The conclusions will be the same.No. The conclusions will be the same.

20.1/1 points | Previous AnswersBBUnderStat11 8.2.024.Ask Your Teacher

My Notes

Compare statistical testing with legal methods used in a U.S. court setting. Then discuss the following topics in class or consider the topics on your own. Please write a brief but complete essay in which you answer the following questions.(a) In a court setting, the person charged with a crime is initially considered to be innocent. The claim of innocence is maintained until the jury returns with a decision. Explain how the claim of innocence could be taken to be the null hypothesis. Do we assume that the null hypothesis is true throughout the testing procedure?
What would the alternate hypothesis be in a court setting?

(b) The court claims that a person is innocent if the evidence against the person is not adequate to find him or her guilty. This does not mean, however, that the court has necessarily proved the person to be innocent. It simply means that the evidence against the person was not adequate for the jury to find him or her guilty. How does this situation compare with a statistical test for which the conclusion is “do not reject” (i.e., accept) the null hypothesis?
What would be a type II error in this context?

(c) If the evidence against a person is adequate for the jury to find him or her guilty, then the court claims that the person is guilty. Remember, this does not mean that the court has necessarily provedthe person to be guilty. It simply means that the evidence against the person was strong enough to find him or her guilty. How does this situation compare with a statistical test for which the conclusion is to “reject” the null hypothesis?
What would be a type I error in this context?

(d) In a court setting, the final decision as to whether the person charged is innocent or guilty is made at the end of the trial, usually by a jury of impartial people. In hypothesis testing, the final decision to reject or not reject the null hypothesis is made at the end of the test by using information or data from an (impartial) random sample. Discuss these similarities between statistical hypothesis testing and a court setting.

(e) We hope that you are able to use this discussion to increase your understanding of statistical testing by comparing it with something that is a well known part of our American way of life. However, all analogies have weak points. It is important not to take the analogy between statistical hypothesis testing and legal court methods too far. For instance, the judge does not set a level of significance and tell the jury to determine a verdict that is wrong only 5% or 1% of the time. Discuss some of these weak points in the analogy between the court setting and hypothesis testing.

Score: 1 out of 1

Comment:

21.–/9 pointsBBUnderStat11 8.2.025.Ask Your Teacher

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Is there a relationship between confidence intervals and two-tailed hypothesis tests? Let c be the level of confidence used to construct a confidence interval from sample data. Let α be the level of significance for a two-tailed hypothesis test. The following statement applies to hypothesis tests of the mean.For a two-tailed hypothesis test with level of significance α and null hypothesis H₀: μ = k, we reject H₀ whenever k falls outside the c = 1 − α confidence interval for μbased on the sample data. When k falls within the c = 1 − α confidence interval, we do not reject H₀.

(A corresponding relationship between confidence intervals and two-tailed hypothesis tests also is valid for other parameters, such as p, μ₁ − μ₂, or p₁ − p₂, which we will study later.) Wh