Question

Public Policy Polling recently conducted a survey asking adults across the U.S. about music preferences. When asked, 80 of the 571 participants admitted that they have illegally downloaded music. You believe that less than 15% of adults across the US download music illegally. Conduct the test at at α = 0.01 level.

1. State the null and alternate hypotheses clearly.
2. Conduct the hypothesis test based on the test statistic and critical value(s). Clearly indicate each.
3. What is the p-value? Use the p-value to conduct the same test
4. Report your conclusion in words, in the context of the problem.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis: p = 0.15
Alternative Hypothesis: p < 0.15

Rejection Region
This is left tailed test, for α = 0.01
Critical value of z is -2.33.
Hence reject H0 if z < -2.33

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.1401 - 0.15)/sqrt(0.15*(1-0.15)/571)
z = -0.663

P-value Approach
P-value = 0.2537
As P-value >= 0.01, fail to reject null hypothesis.

Rejection Region Approach
As the value of test statistic, z is within critical value range, fail to reject the null hypothesis

Conclusion
There is not sufficient evidence to conclude that less than 15% of adults across the US download music illegally