Question

Complete the hypothesis tests using the p-value method. a. State the hypotheses using correct notation. b. Calculate the test statistic. c. Find the p-value. d. Comparing the p-value to the significance level, state and interpret the results. A sample of 800 items produced on a new machine showed that 48 of them are defective. The factory will get rid the machine if the data indicates that the proportion of defective items is significantly more than 5%. At a significance level of 10% does the factory get rid of the machine or not?

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.05

H_a : p > 0.05

n = 800

x = 48

= x / n = 48 / 800 = 0.06

P₀ = 0.05

1 - P₀ = 1 - 0.05 = 0.95

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.06 - 0.05  / [(0.05 * 0.95) / 800]

= 1.298

Test statistic = 1.298

P(z > 1.298) = 1 - P(z < 1.298) = 1 - 0.9029 = 0.0971

P-value = 0.0971

= 0.10

P-value <

Reject the null hypothesis .

There is sufficient evidence to that the proportion of defective items is significantly more than 5% .

Yes