ooooo T-Mobile F 10:13 PM wamap.org You wish to test the following claim (Ha) at

Question

ooooo T-Mobile F 10:13 PM wamap.org You wish to test the following claim (Ha) at a significance level of a 0.02 Ho:p 0.51 Ha: p f 0.51 You obtain a sample of size n 179 in which there are 101 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 t What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic C The test statistic is...

Explanation / Answer

Answer to the question)

p = 0.51

Sample proportion P^ = 101/179 = 0.5642

sample size n = 179

given alpha = 0.02 , and it is two tailed test

So from the Z table we get to know the Z critical value as : 2.33

Since it is a two tailed test: the two critical values are : -2.33 and +2.33

.

The test statistic can be calculated as follows:

Z = (0.5642-0.51) / square root (0.51*0.49/179)

Z = 1.45....[Test Statistic]

.

Since the Z statistic value is 1.45 , it lies between -2.33 and +2.33

thus it does not lie in the critical region

.

Since the Test statistic does not fall in the critical region

We fail to reject the null

.

The last option is correct:

there is not sufficient evidence to support the claim that the population proportion is not equal to 0.51

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