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According to a U.S. news poll, 38% of students in the class of 2013 had done an internship during their time as an undergraduate student. Dana is interested in finding out whether students at her university had an internship rate that was higher than the national average. She decided to ask 100 architecture majors whether they had ever done an internship while at their university. She collected the responses and calculated that the proportion for her university was 43%.Which one of the following statements about the z-test is correct? It is not safe to use the z-test for p, since n * po is not large enough. It is not safe to use the z-test for p, since the sample is not a random sample from the entire population (or cannot be considered as one). It is not safe to use the z-test for p, since n * (1 − po) is not large enough. It is safe to use the z-test for p.

Question

According to a U.S. news poll, 38% of students in the class of 2013 had done an internship during their time as an undergraduate student. Dana is interested in finding out whether students at her university had an internship rate that was higher than the national average. She decided to ask 100 architecture majors whether they had ever done an internship while at their university. She collected the responses and calculated that the proportion for her university was 43%.Which one of the following statements about the z-test is correct? It is not safe to use the z-test for p, since n * po is not large enough. It is not safe to use the z-test for p, since the sample is not a random sample from the entire population (or cannot be considered as one). It is not safe to use the z-test for p, since n * (1 − po) is not large enough. It is safe to use the z-test for p.

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Solution

The z-test can be used in this scenario. The z-test is appropriate when you are dealing with large sample sizes (n > 30). In this case, Dana has a sample size of 100, which is large enough. The conditions for a z-test, which include a random, independent sample and a large enough sample size, are met. Therefore, it is safe to use the z-test for p.

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In testing the hypothesesH0: μ = 75HA: μ < 75,if the value of the Z test statistic equals -1.78, then the p-value is:Group of answer choices0.9625.0.375.0.5375.0.4625.

b) What is the z-score of Exam B?

Suppose we are testing the hypotheses H0: 𝜇 = 5 versus Ha:  𝜇 > 5, and the conditions for performing the Z test are satisfied. For Z-score = 1.52, calculate the p-value.

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