Question

A survey of 1001adults in a​ country, asking​ "As you may​ know, as part of its effort to investigate​ terrorism, a federal government agency obtained records from larger telephone and Internet companies in order to compile telephone call logs and Internet communications. Based on what you have heard or read about the​ program, would you say that you approve or disapprove of this government​ program?" Of those​ surveyed, 531said they disapprove.

a. Determine and interpret the sample proportion.

b. At the 10% significance​ level, do the data provide sufficient evidence to conclude that a majority​ (more than​ 50%) of adults in the country disapprove of this government surveillance​ program?

Answer 1

Given:

Sample size (Number of adults) = n = 1001

Number of adults disapprove = x = 531

a)Sample proportion:

b)

Null and alternative hypothesis:

This corresponding to a right-tailed test, for which a z-test for one population proportion needs to be used.

Test statistic:

Using the P-value approach:

P(Z>1.928) = 0.0269

The p-value is p = 0.0269 …Using standard normal table

And α = 0.10

Since p = 0.0269<0.10, it is concluded that the Null Hypothesis is rejected.
Conclusion: It is concluded that the null hypothesis is rejected. Therefore, there is enough evidence to claim that majority​ (more than​ 50%) of adults in the country disapprove of this government surveillance​ program at 0.10 level of significance.

Done