Question

You wish to test the following claim ( H a ) at a significance level of α = 0.10 . H o : p = 0.76 H a : p > 0.76 You obtain a sample of size n = 178 in which there are 147 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.)

What is the test statistic for this sample? (Report answer accurate to three decimal places.)

Answer 1

You wish to test the following claim ( H _a ) at a significance level of α = 0.10 .

H₀ : p = 0.76     vs H_a : p > 0.76

Here sample size, n=178 and no. of successful observations= 147, then sample proportion estimate,

To test the hypothesis we use a one sample proportion test:

Critical Value =

Test statistic:

which has a standard normal distribution under the null hypothesis. p₀ = proportion value under H₀

We reject the null hypothesis when computed value of T > critical value.

So,Computer value of test statistic = 2.486

Hence, we reject the null hypothesis at 0.1 level of significance.