Question

1. A newspaper published an article about a study in which researchers subjected laboratory gloves to stress. Among 213 vinyl​ gloves, 63​% leaked viruses. Among 213 latex​ gloves, 9​% leaked viruses. Using the accompanying display of the technology​ results, and using a 0.10 significance​ level, test the claim that vinyl gloves have a greater virus leak rate than latex gloves. Let vinyl gloves be population 1.

technology results: Pooled​ proportion: 0.36

Test​ statistic, z: 11.6982

Critical​ z: 1.2816

​ P-value: 0.0000

80% Confidence​ interval:

0.4954473 <p 1 − p 2 <0.5937545

What are the null and alternative​ hypotheses?

Identify the test statistic:

Identify the​ P-value:

2. Rhino viruses typically cause common colds. In a test of the effectiveness of​ echinacea, 32 of the 38 subjects treated with echinacea developed rhinovirus infections. In a placebo​ group, 76 of the 93 subjects developed rhinovirus infections. Use a 0.01 significance level to test the claim that echinacea has an effect on rhinovirus infections. Complete parts​ (a) through​ (c) below.

a. Test the claim using a hypothesis test.

Consider the first sample to be the sample of subjects treated with echinacea and the second sample to be the sample of subjects treated with a placebo. What are the null and alternative hypotheses for the hypothesis​ test?

Identify the test statistic:

Identify the​ P-value:

b. Test the claim by constructing an appropriate confidence interval.

The 99​% confidence interval is:

3. In a random sample of​ males, it was found that 17 write with their left hands and 219 do not. In a random sample of​ females, it was found that 68 write with their left hands and 436 do not. Use a 0.01

significance level to test the claim that the rate of​ left-handedness among males is less than that among females. Complete parts

Test the claim using a hypothesis test.

Consider the first sample to be the sample of subjects treated with echinacea and the second sample to be the sample of subjects treated with a placebo. What are the null and alternative hypotheses for the hypothesis​ test?

Identify the test statistic:

Identify the​ P-value:

b. Test the claim by constructing an appropriate confidence interval.

4. Use the expression in the accompanying discussion of sample size to find the size of each sample if you want to estimate the difference between proportions of men and women who own smartphones. Assume that you want 90​% confidence that your error is no more than 0.03.

The sample should include nothing ___ men and ____ women.

Answer 1