For questions 29-32, a researcher is interested in what fraction of a blog\'s vi

Question

For questions 29-32, a researcher is interested in what fraction of a blog's visitors purchase a product recommended on that blog using the links provided. She samples the records for 100 visitors to test thecurrent assumption that 6% of blog visitors make such a purchase. Of her sample of 100, ten actually made a purchase.

29. Design a hypothesis test for this claim at 95% confidence. What are the null and alternative

hypotheses?
a) H0: p = 0.06 Ha: p 0.06
b) H0: p > 0.06 Ha: p < 0.06

c) H0: p > 0.06 Ha: p <0.06

d) H0: p < 0.06 Ha: p > 0.06

e) H0: p < 0.06 Ha: p > 0.06

30.  Design a hypothesis test for this claim at 95% confidence. What is the value of the teststatistic?
a) z=1.96

.10.06
(.50(1.50)/100)

b) z=1.96

.10.06
(.10(1.10)/100)

c) z=1.96

.10.06
(.06(1.06)/100)

d) z=

.10.06
(.10(1.10)/100)

e) z=.10.06

(.06(1.06)/100)

31) Design a hypothesis test for this claim at 95% confidence. What is the p-value for this claim?

a) 2.5%

b) 4.65%
c) 9.3%

d) 10%

e) 18.36%

32. Design a hypothesis test for this claim. What is a proper statistical conclusion in this case?
a) Because the p-value is small enough, we reject the null hypothesis
b) Because the p-value is large enough, we reject the null hypothesis.

c) Because the p-value is too small, we fail to reject the null hypothesis

d) Because the p-value is too large, we fail to reject the null hypothesis

e) None of the above

Explanation / Answer

Solution:-

Answers => (a), (e), (c), and (d)

Explanation:-

The solution to this problem takes four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. We work through those steps below:

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

Null hypothesis: P = 0.06
Alternative hypothesis: P 0.06

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 0.05. 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 ] = sqrt [(0.06 * (1 - 0.06)) / 100] = 0.02374868417
z = (p - P) / = (0.10 - 0.06)/0.02374868417 = 1.68430384242 or 1.6843

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

We use the Normal Distribution Calculator to find P(z < 1.6843)

The P-Value is 0.092524 or 9.3%
The result is not significant at p < 0.05.

Interpret results. Since the P-value (0.09) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Conclusion. Because the p-value is too large, we fail to reject the null hypothesis.

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