Question

Bob claims that the population proportion of good lemons is p=0.40. To test Bob's claim, we take a simple random sample size of n=180 from this population. In the sample, there are x=73 good lemons.Use the information from the sample to test Bob's claim at the a(alpha symbol)=0.01 significance level. Report the final result of the test.

Hint: answer is either a) reject the null hypothesis H_o or b) cannot reject the null hypothesis H_o

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.40

H_a : p 0.40

= x / n = 73 / 180 = 0.4056

P₀ = 0.40

1 - P₀ = 0.60

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.4056 - 0.40 / [(0.40 * 0.60) / 180]

= 0.15

P(z > 0.15) = 1 - P(z < 0.15) = 0.4404

P-value = 0.8808

= 0.01

P-value >

Fail to reject the null hypothesis .