Conduct a test at the alphaequals0.05 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 greater than p 2. The sample data are x 1 equals 122, n 1 equals 244, x 2 equals 137, and n 2 equals 311.

There is not enough evidence to reject the null hypothesis.

Step-by-step explanation:

(a)

The hypothesis can be defined as follows:  

H₀: p₁ - p₂ ≤ 0 vs. Hₐ: p₁ - p₂ > 0.  

(b)

The test statistic is defined as follows:

The information provided is:

n₁ = 244

n₂ = 311

x₁ = 122

x₂ = 137

Compute the sample proportions and total proportions as follows:

Compute the test statistic value as follows:

The test statistic value is 1.41.

The decision rule is:

The null hypothesis will be rejected if the p-value of the test is less than the significance level α = 0.05.

Compute the p-value as follows:

*Use a z-table.

The p-value of the test is 0.08.

p-value = 0.08 > α = 0.05

The null hypothesis will not be rejected at 5% significance level.

Thus, there is not enough evidence to reject the null hypothesis.

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