Question

Consider the following hypothesis test:

H0: p ? 0.75
Ha: p < 0.75

A sample of 400 items was selected. Compute the p-value and state your conclusion for each of the following sample results. Use ? = .05.

Round your answers to four decimal places.

1. p = 0.61 find p-value

2. p = 0.75 find p-value

3. p = 0.78 find p-value

Answer 1

Given that, sample size (n) = 400

Significance level = 0.05

Null and alternative hypotheses are,

1) Given p = 0.61

Test statistic is,

P-value = P(Z < -6.47) = 0.000

Here, p-value = 0.0000 < 0.05

implies that, we reject the null hypothesis (H0).

2) Given p = 0.75

Test statistic is,

P-value = P(Z < 0) = 0.5000

Here, p-value = 0.5000 < 0.05

implies that, we fail to reject the null hypothesis (H0).

3) Given p = 0.78

Test statistic is,

P-value = P(Z < 1.39) = 0.9177

Here, p-value = 0.9177 < 0.05

implies that, we fail to reject the null hypothesis (H0).