Wiki Page, Math 13 - Perez Sandbox : ANSWER(S): Module 24 - Hypothesis Test for a Population Mean Lab (4c of 5 discussion 1)

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

1. We would like to test whether or not is the same as the national mean (4.73) and therefore we are testing the following hypotheses.

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2. Yes, we can safely use the t-test. The conditions are met since: (i) The sample is random and (ii) The sample size is large enough (n = 75) for the Central Limit Theorem to kick in. Therefore, sample means vary normally in this situation, despite the fact that the distribution of the variable of interest (number of alcoholic drinks per week) is skewed to the right in the sample with outliers.

3. From the StatCrunch results

One sample T hypothesis test: : Mean of variable
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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

we see that the test statistic is T = –1.83 and the P-value is 0.072. At the 5% level of significance, we fail to reject the null hypothesis. The results are not statistically significant.

4. We cannot conclude that the mean number of alcoholic drinks that students at the liberal arts college consume in a typical week is different from 4.73 (the mean of college students in general). The difference observed in this sample is not statistically significant.

5. Explanations of Std. Err, T-stat, P-value

1. Std. Err (standard error): The average deviation of sample means from the hypothesized population mean of 4.73 drinks is about 0.44 drinks.

2. T-stat (T-score): The observed sample mean of 3.93 drinks is 1.8 standard errors below the hypothesized population mean of 4.73 drinks.

3. P-value: If the population mean is 4.73 drinks, there is a 7.2% chance that sample means will have an error larger than that observed in our sample (observed error = 4.73 – 3.93 = 0.8 drinks) when selecting random samples of 75 students.