Question 10 of 10 (1 point) View problem in a pop-up For Americans using library

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Question 10 of 10 (1 point) View problem in a pop-up For Americans using library services, the American Library Association (ALA) claims that 67% borrow books. A library director feels that this is not true, so he randomly selects 95 borrowers and finds that 77 borrowed books. Can he show that the ALA claim is incorrect? Use = 0.10. Part 1 out of 5 State the hypotheses and identify the claim with the correct hypothesis : p (select1] (select) 1. Hi! p (select) D ] (select) -- This hypothesis test is a (select) test. NEXT

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Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P = 0.67
Alternative hypothesis: P 0.67

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample proportion is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.10. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation () and compute the z-score test statistic (z).

= sqrt[ P * ( 1 - P ) / n ]

= 0.04824
z = (p - P) /

z = 2.91

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the z-score is less than - 2.91 or greater than 2.91.

Thus, the P-value = 0.0036

Interpret results. Since the P-value (0.0036) is less than the significance level (0.10), we have to reject the null hypothesis.

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