Question

Use the normal distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from a random sample and use a 5 % significance level. Test Upper H Subscript 0 Baseline : p equals 0.5 vs Upper H Subscript a Baseline : p greater-than 0.5 using the sample results p Overscript ^ EndScripts equals 0.56 with n equals 39 Round your answer for the test statistic to two decimal places, and your answer for the p-value to three decimal places. test statisticequals p-valueequals Conclusion:

Answer 1

Solution:-

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.

Formulate an analysis plan. For this analysis, the significance level is 0.05. 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 (S.D) and compute the z-score test statistic (z).

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

S.D = 0.04003
z = (p - P) / S.D

z = 1.499

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 greater than 1.499.

Thus, the P-value = 0.067.

Interpret results. Since the P-value (0.067) is greater than the significance level (0.05), we have to accept the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that proportion is greater than 0.50.