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Hypothesis Test for Means

1. The mean age of bus drivers in Chicago is 54.5 years. If a hypothesis test is performed, how should you interpret a decision that fail to rejects the null hypothesis?

A There is sufficient evidence to reject the claim mean = 54.5
B There is not sufficient to reject the claim mean = 54.5
C There is sufficient evidence to support the claim mean = 54.5
D There is not sufficient evidence to support the claim mean = 54.5

2. The dean of a major university claims that the mean times for students to earn a Bachelor's degree is at most 5 years. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?

A There is sufficient evidence to reject the claim population mean is less than or equal to 5
B There is not sufficient evidence to reject the claim population mean is less than or equal to 5
C There is sufficient evidence to support the claim population mean is less than or equal to 5
D There is not sufficient evidence to support the claim population mean is less than or equal to 5

4. Suppose you want to test the claim that the two means from two populations are equal. Two samples are randomly selected from each population. The sample statistics are given below. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis? Use alpha=0.05.

Solution Preview

In general, when you get results that lead you to reject the null hypothesis (i.e. the p-value you get is very low), you say something like "we can reject the null hypothesis and accept the alternative hypothesis". This doesn't mean that you think the alternative hypothesis is definitely true; it just means that you think that the null hypothesis is so unlikely that you can safely reject it. When you get results that fail to reject the null hypothesis, you say something like "we cannot reject the null hypothesis". This doesn't mean that the null hypothesis is true, just that you don't have enough evidence to reject it.

1. The mean age of bus drivers in Chicago is 54.5 years. If a hypothesis test is performed, how should you interpret a decision that fail to rejects the null hypothesis?

Here, the null hypothesis is that the mean age is 54.5 years (this is the default assumption), and ...

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