Question

west high school is a large school with more than \[2{,}000\] students. the school requires that students are assigned an average of \[3.5\] hours of homework each night. the school board believes that students are being assigned less than this, so they take a random sample of \[50\] west high school students to determine if there is convincing evidence to support their suspicion. the homework times in the sample are strongly skewed to the right. the school board wants to use these sample data to conduct a \[t\] test about the mean. which conditions for performing this type of test did their sample meet?

Answer 1

The sample meets the conditions for conducting a t-test about the mean, except for the assumption of normality.

Step-by-step explanation:

In order to conduct a t-test about the mean, certain assumptions or conditions must be met:

1. The sample should be randomly selected: The problem states that the school board took a random sample of 50 students, so this condition is met.
2. The sample should be independent: Since each student is selected independently and the sample size is less than 10% of the population, this condition is also met.
3. The sample should be sufficiently large: The problem states that the school is large, with more than 2,000 students. While the specific sample size is not mentioned, we can assume that it is large enough for the t-test to be valid.
4. The distribution of the sample should be approximately normal: The problem states that the homework times in the sample are strongly skewed to the right. Skewness can affect the validity of the t-test, so this condition is not met.

Based on the provided information, the sample meets the conditions for conducting a t-test about the mean, except for the assumption of normality.