A professor believes that, for the introductory art history classes at his university, the mean test score of students in the evening classes is lower than the mean test score of students in the morning classes. He collects data from a random sample of 250 students in evening classes and finds that they have a mean test score of 85.6. He knows the population standard deviation for the evening classes to be 4.6 points. A random sample of 150 students from morning classes results in a mean test score of 86.7. He knows the population standard deviation for the morning classes to be 8.3 points. Test his claim with a 99 % level of confidence. Let students in the evening classes be Population 1 and let students in the morning classes be Population 2. Step 2 of 3: Compute the value of the test statistic. Round your answer to two decimal places.

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**Hypothesis Testing in Introductory Art History Classes**

A professor believes that, for the introductory art history classes at his university, the mean test score of students in the evening classes is lower than the mean test score of students in the morning classes. He collects data from a random sample of 250 students in evening classes and finds that they have a mean test score of 85.6. He knows the population standard deviation for the evening classes to be 4.6 points. A random sample of 150 students from morning classes results in a mean test score of 86.7. He knows the population standard deviation for the morning classes to be 8.3 points. Test his claim with a 99% level of confidence. Let students in the evening classes be Population 1 and let students in the morning classes be Population 2.

**Step 2 of 3:** Compute the value of the test statistic. Round your answer to two decimal places.

--- 

In this scenario, the professor aims to statistically test whether the mean score of evening students is indeed lower than that of morning students by using a hypothesis test with a 99% confidence level. This involves calculating the test statistic based on the sample means, population standard deviations, and sample sizes provided. This analysis will help ascertain the likelihood of observing the sample means if the null hypothesis (no difference in means) were true.
Transcribed Image Text:**Hypothesis Testing in Introductory Art History Classes** A professor believes that, for the introductory art history classes at his university, the mean test score of students in the evening classes is lower than the mean test score of students in the morning classes. He collects data from a random sample of 250 students in evening classes and finds that they have a mean test score of 85.6. He knows the population standard deviation for the evening classes to be 4.6 points. A random sample of 150 students from morning classes results in a mean test score of 86.7. He knows the population standard deviation for the morning classes to be 8.3 points. Test his claim with a 99% level of confidence. Let students in the evening classes be Population 1 and let students in the morning classes be Population 2. **Step 2 of 3:** Compute the value of the test statistic. Round your answer to two decimal places. --- In this scenario, the professor aims to statistically test whether the mean score of evening students is indeed lower than that of morning students by using a hypothesis test with a 99% confidence level. This involves calculating the test statistic based on the sample means, population standard deviations, and sample sizes provided. This analysis will help ascertain the likelihood of observing the sample means if the null hypothesis (no difference in means) were true.
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