In Exercises 13 and 14, (d) decide whether to reject or fail t...

Question

In Exercises 13 and 14, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.

Use

[APPLET] A highway patrol officer stops speeding vehicles on an interstate highway. The genders of the last 25 drivers who were stopped are shown, where F represents a female driver and M represents a male driver. Can you conclude that the stops were not random by gender?

F M M M F M F M F F F M M

F F F M M M F M M F F M

Accepted Answer

All right. Hello everyone. So this question says, in a library study, the next 24 borrowed books are recorded. If the books were borrowed randomly by genre. You would expect a 50/50 split between fiction and nonfiction. However, only 7 of the books are fiction. Assume n equals 24. P equals 0.5 and use a two-tailed test with alpha equals 0.05. The critical values for this test are. X less than or equal to 8, or X greater than or equal to 16. Should you reject the null hypothesis, what do you conclude about the borrowing pattern? So first and foremost, what are the hypotheses that are being tested in this problem? Well, notice how the text of the question says that. If the books were borrowed randomly, we would expect a 50 to 50 split between fiction and nonfiction. That therefore is the null hypothesis. So the null hypothesis would state that P is equal to 0.5, which tells you that the borrowing is random between fiction and nonfiction. And so the alternative hypothesis would state the opposite. Instead, it would state that P is not equal to 0.5, which tells you that borrowing is not random between the two genres. And, as mentioned before, this is a two-tilt test. So, we already have both the observed value and the critical region. So the observed fiction books represented by the variable X is equal to 7. So, according to the critical values that we are given, we would reject the null hypothesis, so long as X is less than or equal to 8, or if X is less than, or excuse me, greater than or equal to 16. And indeed, X equals 7 is in fact less than 8, which means that we can reject. A not we can reject the null hypothesis. So how does this. How does this translate to a conclusion? Well, because we've rejected the null hypothesis, we would state that there is significant evidence that borrowing is not random with respect to the genre. And specifically, fewer fiction books were borrowed than expected under the randomness assumption. So now this brings you to the final answer, which I've pre-written here on the screen. The final answer reads as follows. Reject H knot, borrowing is not random by genre. And there you have the So with that being said, thank you so very much for watching and I hope you found this helpful.

Key Concepts

Null Hypothesis

Statistical Significance

Interpretation of Results

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