hypothesis test for a population mean i give you eaxample make same one but diffrenet words

Learn by Doing

This activity gives you practice explaining the different parts of the StatCrunch print-out for a hypothesis test for a population mean. You will review the meaning of standard error, T-scores and the P-value.

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Prompt

1. In a previous lab we tested the following hypotheses,
   $H$ 0:
   $\mu$ = 4.73 and
   $H$ a:
   $\mu$ < 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
   
   $H_{}$ 0:
   $\mu$ = 4.73
   
   $H$ A:
   $\mu$ ≠ 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
4. 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:
   
   $\mu$ D = μ 1 − μ 2: Mean of the difference between Regular seed and Kiln-dried seed
   
   $H$ 0:
   $\mu$ D = 0
   
   $H$ A:
   $\mu$ 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.

   Example to rigth answer { hint }

1.) a. The Standard error is 0.44 which means that the sample means deviate .44 drinks away from the population mean of 4.73 drinks.

b. The T-stat is -1.83 which means that the sample mean is 1.8 standard errors below the population mean of 4.73 drinks, which equals 3.93 drinks.

c. The P-value is 0.07 so if the population mean is 4.73 drinks, when we select 75 students there is a 7% chance that the sample mean will have a bigger error than the sample (.8)

2.) The standard error is 19.95 which means that the differences in plant yield deviate 19.95 plants from the mean of 33.73 plants.

b. The T-stat is -1.69 which means that the sample mean is 1.69 standard errors below the population mean of differences in plant yield.

c. The P-value is .06 which means that 6% of the time, a random sample of 11 plots of land with a mean difference of 33.73 plants will a larger absolute error than observed in our sample.