Question

A polling agency reports that over 16% of U.S. adults are without health care coverage. In a random survey of 1420 U.S. adults, 256 said they did not have health care coverage. At α = 2%, is there enough evidence to support the agency’s claim?

1. State the null and alternative hypotheses and identify which represents the claim.

2. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. Explain your reasoning and sketch the graph of the problem.

3. Find the p-value using 1-PropZTest.

4. Explain how you should interpret your decision about the null hypothesis.

5. Your conclusion?

Answer 1

Proportion (p0) = 0.16

Total number of sample (n) = 1420

number of favourable events (X) = 256

We are interested in testing the hypothesis

Since P-value of a two tailed test is equal to

P = (1-0.9814517296666775)

P = 0.0185

Since, the test is two-tail test at \alpha = 0.02

Decision Rule: Reject the null hypothesis if the test statistic value is greater than the critical value 2.0537489106318225

The statistic value, 2.0847 is greater than the critical value 2.0537489106318225. Hence, reject the null hypothesis.

It is true that polling agency reports that over 16% of U.S. adults are without health care coverage