You wish to test the following claim (H_a) at a significance level of alpha = 0.

Question

You wish to test the following claim (H_a) at a significance level of alpha = 0.02. H_o:p = 0.77 H_a:p notequalto 0.77 You obtain a sample of size n = 498 in which there are 392 successful observations. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution. What is the critical value for this test? (Report answer accurate to three decimal places.) critical value = plusminus What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic =

Explanation / Answer

Solution:-

x = 392, n = 498

p = 392/498

p = 0.787

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

Null hypothesis: P = 0.77

Alternative hypothesis: P 0.77

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample proportion is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.02. 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 ]

= 0.01886

z = (p - P) /

z = 0.909

zcritical = + 2.326

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

Interpret results. Since the z test(0.909) is less than the zcritical (2.326), we cannot reject the null hypothesis.

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