Question

The Pew Research Center reported in 2018 that 68% of U.S. adults rated "reducing health care costs" as a national priority. This year a survey is conducted with a national sample of 1,505 U.S. adults selected by a combination of landline and cell phone random digit dials. This year's survey finds that 70% of the sample says that "reducing health care costs" is a national priority. We test the following hypotheses: LaTeX: H_0 H 0 : The proportion of U.S. adults this year who rate "reducing health care costs" as a national priority is still 0.68. LaTeX: H_a H a : The proportion of U.S. adults this year who rate "reducing health care costs" as a national priority is greater than 0.68. The P-value is 0.045. At a 5% significance level, we would reject the null hypothesis and concluded that the proportion of U.S. adults this year who rate "reducing health care costs" as a national priority is greater than 0.68. Explain the P-value in the context of this issue.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.68

H_a : p > 0.68

n = 1505

=0.70

P₀ = 0.68

1 - P₀ = 1-0.68 = 0.32

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

=0.70-0.68 / [0.68*(0.70) /1505 ]

= 1.66

P(z >1.66 ) = 1 - P(z <1.66) = 0.0485

P-value = 0.0485

= 0.05    

0.0485 < 0.05

Reject the null hypothesis .

There is sufficient evidence to suggest that