Question

A recent survey of 500 men and 500 women showed that 37% of men owned guns and 31% of women owned guns. What is the hypothesis test for whether gun ownership is greater for men, where

a. H0:D≠0;HA:D=0H0:D≠0;HA:D=0

b. H0:D≥0;HA:D<0H0:D≥0;HA:D<0

c. H0:D=0;HA:D≠0H0:D=0;HA:D≠0

Using the sample sizes and sample proportions above what is the value of the test statistic for the hypothesis test?

a. -1.534

b. .0299

c. 2.007

d. 1.645

Assume the test statistic was found to be 2.21, what would p-value and outcome of the test be at the 99% confidence level assuming the hypothesis test was found to be the following:

Assume the test statistic was found to be 2.21, what would p-value and outcome of the test be at the 99% confidence level assuming the hypothesis test was found to be the following:

a. .9864; Fail to Reject the Null Hypothesis

b. .9728; Reject the Null Hypothesis

c. .0272; Fail to Reject the Null Hypothesis

d. .0136; Reject the Null Hypothesis

What are the critical values for the 10%, 5% and 1% significance levels using the hypothesis test that follows:

a. ±1.65,±1.96,±2.58±1.65,±1.96,±2.58±1.65,±1.96,±2.58

b. ±1.29,±1.65,±2.33±1.29,±1.65,±2.33±1.29,±1.65,±2.33

c. ±1.29,±1.96,±2.33±1.29,±1.96,±2.33±1.29,±1.96,±2.33

Answer 1

Q.1.

In two samples of equal size, where D denotes the difference in gun ownership between men and women, hypothesis test for whether gun ownership is greater for men is given by:

H0:D≥0;HA:D<0

Correct Ans - b

Q.2.

Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).

0.375000.31 500 P1n1P2n2 = 0.34 500500 n1n2

SE Vp* (1- p) * [1/n1 1/n2] = V0.34 0.66 2/500 0.03

0.37- 0.31 Pi P2 = 2 SE 0,03

where p₁ is the sample proportion in sample 1, where p₂ is the sample proportion in sample 2, n₁ is the size of sample 1, and n₂ is the size of sample 2.

Correct Ans - c

Q.3.

• Since we have a one-tailed test, the P-value is the probability that the z-score is less than 2.21 (test statistic). We use the Normal Distribution Calculator to find P(z < 2.21). The P-Value is .013553.
• Interpret results. Since the P-value (0.0136) is greater than the significance level (0.01), we cannot reject the null hypothesis.

Correct Ans - d

(Though it seems error in the option)