Question

Testing Claims You wish to test the following claim ( H a ) at a significance level of α = 0.001 . H o : p = 0.71 H a : p < 0.71 You obtain a sample of size n = 636 in which there are 420 successful observations. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = 0.573 Incorrect What is the p-value for this sample? (Report answer accurate to three decimal places.) p-value = 0.567 Incorrect

Answer 1

Solution:-

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

Null hypothesis: P > 0.71
Alternative hypothesis: P < 0.71

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 = 0.01799
z = (p - P) / S.D

z = - 2.758

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 -2.758.

Thus, the P-value = 0.008

Interpret results. Since the P-value (0.008) is less than the significance level (0.05), we have to reject the null hypothesis.