A recent study indicated that 17 percent of adults in the country actively seek out science news sites to keep current on topics in science. A university researcher believes that percent is too low. From a random sample of adults in the country, the researcher found that 22 percent of the sample actively seek out science news sites. Which of the following is the most appropriate method for the researcher’s study?

A) A two-sample z-test for a difference in population proportions
B) A two-sample z -test for a difference in population proportions
C) A one sample z-test for a difference in population proportions
D) A one sample z-test for a sample proportion
E) A one sample z-test for a population proportion

A statistical test that helps to determine whether the two population means are different when the variances are known and the sample size is large. This statistical test is known as Z-test.

One-Sample Z-test

It is used when we want to know whether the difference between the mean of a sample and the population is large enough to be significant statistically, that is if it is unlikely to have occurred by chance.

The test is performed to check the violations of normal distribution and it is usually used for large sample size (N > 30), or when the population variance is known.

Given to us,

A recent study indicated that 17 percent of adults in the country actively seek out science news sites to keep current on topics in science.
From a random sample of adults in the country, the researcher found that 22 percent of the sample actively seek out science news sites.

From Statement 1,

The null hypothesis will be,

[tex]H_0 <0.2[/tex]

From Statement 2,

The alternate hypothesis will be,

[tex]H_1>0.2[/tex]

Conclusion

So, we can say that the test is left-tailed or oriented.

Hence, the correct statement should be "A one-sample z -test for a sample proportion".

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