Wiki Page, Math 13 - Perez Sandbox : ANSWER(S): Module 24 - Hypothesis Test for a Population Mean (5a of 5 discussion 3)

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2026-01-17T21:14:50-08:00

1. Hypothesis test for the mean number of alcoholic drinks consumed a week by students at a liberal arts college:

1. Standard error: The estimated standard error is 0.44. This tells us that on average random samples of 75 students have 0.44 error in their estimates of alcoholic drinks consumed per week when the population mean is 4.73 drinks per week.

2. T-stat: A T-stat of -1.83 tells us that the sample mean (3.93 alcoholic drinks a week) is 1.83 standard errors below the hypothesized population mean given in the null hypothesis (4.73).

3. P-value: Here are a couple of ways to describe the P-value.

There is a 7.2% chance that random samples of this size (n=75) will have more absolute error than observed in this sample. For this sample, the mean number of drinks differed from the hypothesized mean for the population of all students at this college by -0.8 (3.93 - 4.73); in other words, the absolute error in our sample is 0.8. In random samples of 75 students from this population, we will see sample means with a greater absolute error than observed in our sample about 7.2% of the time.
OR
If students at this college consume an average of 4.73 alcoholic drinks a week, then it is somewhat common to see samples of 75 students consuming on average fewer than 3.93 drinks or more than 5.53 drinks a week. This happens about 7.2% of the time.

2. Matched pairs hypothesis test for difference in corn yields:

1. StatCrunch gives a standard error of about 19.95; this is what we have been calling the estimated standard error. It is the average amount of error in samples of this size due to chance (expected variation in random samples.) It tells us that, on average, samples of this size will have differences in yields of about 20 if there really is no difference between the kiln-dried and regular seeds.

2. The test statistic is -1.69. It tells us that the differences in corn yields observed in this experiment are about 1.69 standard errors below the hypothesized mean of 0 (no difference).

3. The P-value indicates that there is a 6.1% chance of observing absolute differences larger than those observed in this experiment if there was really no difference between regular and kiln-dried seeds (as the null hypothesis claims).