In a recent court case it was found that during a period of 11 years 867 people

Question

In a recent court case it was found that during a period of 11 years 867 people were selected for grand jury duty and 39% of them were from the same ethnicity. Among the people eligible for grand jury duty, 78.9% were of this ethnicity. Among the people eligible for grand jury duty, 78.9% were of this ethnicity. Use a 0.01 significance level to test the claim that the selection process is biased against allowing this ethnicity to sit on the grand jury. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method and the normal distribution as an approximation to the binomial distribution.

What is the test statistic?

A) z = _ ( round to 2 decimal places )

B ) P value = _ ( round to 2 decimal places)

Choose between Is or Is not

C) There ( Is ) or ( Is not ) sufficient evidence to support the claim that the polygraph results are correct less than 80%of the time.

Explanation / Answer

Solution:-

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

Null hypothesis: P > 0.789

Alternative hypothesis: P < 0.789

Note that these hypotheses constitute a one-tailed test.

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 ]

= 0.01386

z = (p - P) /

z = - 28.8

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 - 28.8.

Thus, the P-value = less than 0.0001

Interpret results. Since the P-value (almost 0) is less than the significance level (0.01), we have to reject the null hypothesis.

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