Mathematics Homework Help

Prompt

1. In a previous lab we tested the following hypotheses, 0$H_0$: =4.73$\mu =4.73$ and $H_a$: <4.73$\mu <4.73$ (where $\mu$ is the mean number of alcoholic drinks consumed by students at a liberal arts college).

   In a random sample of 75 students, the mean was 3.93 alcoholic drinks consumed in a week. Here is the StatCrunch output from the hypothesis test.
   $\mu$: Mean of variable
   0$H_0$: =4.73$\mu =4.73$
   $H_A$: ≠4.73$\mu \ne 4.73$

   Hypothesis test results

   Variable	Sample Mean	Std. Err.	DF	T-Stat	P-value
   number of drinks per week	3.9333333	0.43592434	74	-1.8275343	0.0717

   Using this context and the StatCrunch output, explain the meaning of each of the following.

   1. Std. Err (standard error)
   2. T-stat (T-score)
   3. P-value
2. In a previous matched pairs lab we tested the following hypotheses, where $\mu$ is the mean of the differences in corn yield for a plot of land (regular seed minus kiln-dried): H0: µ = 0 and Ha: µ < 0. In a random sample of 11 seeds of each type, the mean of the differences in the sample was -33.7. Here is a StatCrunch print-out of the hypothesis test.

   Paired T hypothesis test:
   = 1− 2${\mu }_D={\mu }_1-{\mu }_2$: Mean of the difference between Regular seed and Kiln-dried seed
   0$H_0$: =0${\mu }_D=0$
   $H_A$: <0${\mu }_D<0$

   Hypothesis test results

   Difference	Mean	Std. Err.	DF	T-Stat	P-value
   Regular seed – Kiln-dried seed	-33.727273	19.951346	10	-1.6904761	0.0609

   Differences stored in column, Differences.

   Using this context and the StatCrunch output, explain the meaning of each of the following.

   1. Std. Err (standard error)
   2. T-stat (T-score)
   3. P-value.