Determine the test statistic determine the p-value what is

Question

1. Conduct a test at the a = 0.05 level of significance by determining (a) the null and alternative hypotheses, (b) the test statistic, and (c) the P-value. Assume the samples were obtained independently from a large population using simple random sampling.

Test whether p 1 > p₂. The sample data are x ₁= 121, n_i= 254, x₂ = 136, and n₂ = 301.

(a) Choose the correct null and alternative hypotheses below.

• H_o: p_i = 0 versus H_i: p_i 0
• H_o: p_i = p₂ versus H_i: p_i
• Ho: Pi= P2 versus H₁: p_i > p₂
• Ho: p_i = p₂ versus H : p_i P2

(b) Determine the test statistic.

(c) Determine the P-value.

What is the result of this hypothesis test?

• Do not reject the null hypothesis because there is not sufficient evidence to conclude that p ₁ < p₂.
• Reject the null hypothesis because there is sufficient evidence to conclude that p 1 < p₂.
• Do not reject the null hypothesis because there is not sufficient evidence to conclude that p 1 > p2.
• Do not reject the null hypothesis because there is not sufficient evidence to conclude that p ₁ p₂.

2. Construct a confidence interval for p _i - p₂ at the given level of confidence.

x₁ = 392, n_i= 504, x₂ = 417, n₂ = 569, 99% confidence

The 99% confidence interval for p _i - p₂ is ().

3. In a clinical trial of a vaccine, 14,000 children were randomly divided into two groups. The subjects in group 1 (the experimental group) were given the vaccine while the subjects in group 2 (the control group) were given a placebo. Of the 7,000 children in the experimental group, 82 developed the disease. Of the 7,000 children in the control group, 101 developed the disease.

Determine whether the proportion of subjects in the experimental group who contracted the disease is less than the proportion of subjects in the control group who contracted the disease at the a = 0.01 level of significance.

Choose the correct null and alternative hypotheses below.

• Ho: p_{i =p2} ^versus H1: Pi
• H_o: p_i = 0 versus H_i: p_i < 0
• H_o: p_i = p₂ versus H_i: p_i > p₂
• H_o: p_i = p₂ versus 11₁: p_i = P2

Determine the test statistic.

Determine the P-value.

What is the result of this hypothesis test?

• Reject the null hypothesis because there is not sufficient evidence to conclude that the proportion of subjects in the experimental group who contracted the disease is less than the proportion of subjects in the control group at a = 0.01.
• Do not reject the null hypothesis because there is not sufficient evidence to conclude that the proportion of subjects in the experimental group who contracted the disease is less than the proportion of subjects in the control group at a = 0.01.
• Reject the null hypothesis because there is sufficient evidence to conclude that the proportion of subjects in the experimental group who contracted the disease is less than the proportion of subjects in the control group at a = 0.01.
• Do not reject the null hypothesis because there is sufficient evidence to conclude that the proportion of subjects in the experimental group who contracted the disease is less than the proportion of subjects in the control group at a = 0.01.

4. The following data represent the muzzle velocity (in feet per second) of shells fired from a 155-mm gun. For each shell, two measurements of the velocity were recorded using two different measuring devices, resulting in the following data.

Observation A B

1 790.7 787.6

2 790.9 796.2

3 794.1 792.8

4 793.2 797.4

5 791.5 797.3

6 791.6 793.8

(a) Why are these matched-pairs data?

• The same round was fired in every trial.
• Two measurements (A and B) are taken on the same round
• The measurements (A and B) are taken by the same instrument.
• All the measurements came from rounds fired from the same gun.

(b) Is there a difference in the measurement of the muzzle velocity between device A and device B at the a = 0.01 level of significance? Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers. What is your conclusion regarding H_o?

Reject H_o.

Do not reject H_o.

(c) Construct a 99% confidence interval about the population mean difference. Compute the difference as device A minus device B. Interpret your results.

Choose the statement that best agrees with your interpretion of your results.

• I am 99% confident that the mean difference in measurement lies in the interval found above.
• I am 12% confident that the mean difference in measurement is 0.
• I am 1% confident that the mean difference in measurement lies in the interval found above.
• I am 12% confident that the mean difference in measurement is 0.01.