Question

1. According to a recent report, 38% of adults wait until they are 30 years of age or older to get married for the first time. A researcher believes this claimed value is too low. He gathers data in order to test the hypotheses Ho: p = 0.38 vs. Ha: p > 0.38. In these hypotheses, what does p represent?

A. The p-value B. The sample proportion C. The population proportion D. The sample mean E. The population mean


2. A claim is made that college students get an average of 5.8 hours of sleep per weeknight. You believe college students get more than 5.8 hours of sleep per night. You decide to conduct a hypothesis test by surveying a random sample of 50 college students. You find your sample gets an average of 6 hours of sleep per night, with a sample standard deviation of 1 hour. What will the test statistic be? Choose the answer below that is closest to what you calculate.

A. Less than 0.01 B. 0.2 C. 1.0 D. 1.4 E. Larger than 3.4


3. A hypothesis test is conducted and the p-value is 0.044. What will the conclusions be at alpha (or significance) levels of 0.10, 0.05, and 0.01?

A. We will reject Ho if the alpha level is 0.10 but not if the alpha level is 0.05 or 0.01. B. We will reject Ho if the alpha level is either 0.10 or 0.05, but not if the alpha level is 0.01. C. We will reject Ho if the alpha level is 0.10, 0.05, or 0.01. D. We will fail to reject Ho if the alpha level is 0.10, 0.05, or 0.01.

Answer 1

Solution(1)

Given in the question

Null hyothesis H0: p=0.38

Alternate hypothesis p>0.38

Here in this hypothesis p is population proportion

So it's answer C. I.e. population proportion.

Solution(2)

Test stat = (sample mean-population mean)/sample standard deviation/Sqrt(n) = (6-5.8)/1/Sqrt(50) = 1.4

So it's answer is D. I e. 1.4

Solution(3)

We will reject null hypothesis if p-value is less than alpha value.

As we can see we can reject null hypothesis at significance level 0.05 and 0.1 as p-value is less than both levels. While we are failed to reject null hypothesis at 0.01 significance level.

So it's answer is B.