(a) Identify the claim and state H0 and Ha.
(b) Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed, and whether to use a z-test, a t-test, or a chi-square test. Explain your reasoning.
(c) Choose one of the options. If convenient, use technology.
Option 1: Find the critical value(s), identify the rejection region(s), and find the appropriate standardized test statistic.
Option 2: Find the appropriate standardized test statistic and the P-value.
(d) Decide whether to reject or fail to reject the null hypothesis.
(e) Interpret the decision in the context of the original claim.
4. A research center claims that more than 55% of U.S. adults think that it is essential that the United States continue to be a world leader in space exploration. In a random sample of 25 U.S. adults, 64% think that it is essential that the United States continue to be a world leader in space exploration. At a = 0.05, is there enough evidence to support the center’s claim?
(a) The following null and alternative hypotheses for the population proportion needs to be tested:
"H_0:p\\le0.55"
"H_a:p>0.55"
(b) This corresponds to a right-tailed test, for which a z-test for one population proportion will be used.
(c) Based on the information provided, the significance level is "\\alpha = 0.05," and the critical value for a right-tailed test is "z_c = 1.96."
The rejection region for this right-tailed test is "R = \\{z: z > 1.96\\}."
The z-statistic is computed as follows:
Since it is observed that "z =0.9045< 1.96=z_c," it is then concluded that the null hypothesis is not rejected.
Using the P-value approach:
The p-value is "p=P(Z>0.9045)=0.182865," and since "p =0.182865> 0.05=\\alpha," it is concluded that the null hypothesis is not rejected.
Therefore, there is not enough evidence to claim that the population proportion "p" is greater than 0.55, at the "\\alpha = 0.05" significance level.
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