Question

2. A study by a medical researcher of HIV infection rates among injection drug users reported that the rate of new infections steadily dropped over the last couple of decades. The latest report was that 2% of IV drug uses are HIV positive. A drug counselor believes that this trend is continuing and that the percentage of IV drug users in his city who are HIV positive is now less than 2%. The counselor surveys a simple random sample of 415 IV drug users in the city and finds that 8 are HIV positive. Does this evidence support the counselor’s belief? Use a 0.01 level of significance

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#1-4: Complete the hypothesis tests using the traditional method. a. State they hypotheses. b. Calculate the test statistic. c. Find the critical value(s) using the given level of statistic. d. Draw a diagram comparing the critical value to the test statistic. e. State the conclusion and interpret the results.

Answer 1

a. Here claim is that p<0.02

So hypothesis is vs

b. Here

Hence test statistics is

c. The z-critical value for a left-tailed test, for a significance level of α=0.01 is

zc​=−2.33

Graphically

d. As test statistics is not in the rejection region we fail to reject the null hypothesis

e. Hence we do not have sufficient evidence to support the claim that p<0.02