What is p? In a representative sample of 1000 adult Americans, only 450 could na

Question

What is p?

In a representative sample of 1000 adult Americans, only 450 could name at least one justice who is currently serving on the U.S. Supreme Court. Using a significance level of 0.01, carry out a hypothesis test to determine if there is convincing evidence to support the claim that fewer than half of adult Americans can name at least one justice currently serving on the Supreme Court. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = p = The data provides enough evidence to suggest that fewer than half of all adult Americans can name at least one justice currently serving on the Supreme Court. You may need to use the appropriate table in Appendix A to answer this question.

Explanation / Answer

Solution:- p value = 0.0008

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P > 0.50

Alternative hypothesis: P < 0.50

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected only if the sample proportion is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation () and compute the z-score test statistic (z).

= sqrt[ P * ( 1 - P ) / n ]

= 0.0158

z = (p - P) /

z = - 3.16

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Since we have a one-tailed test, the P-value is the probability that the z-score is less than - 3.16. We use the Normal Distribution Calculator to find P(z < - 3.16) = 0.04.

Thus, the P-value = 0.0008

Interpret results. Since the P-value (0.0008) is less than the significance level (0.01), we cannot accept the null hypothesis.

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