Question

Suppose that in a random selection of 100 colored​ candies, 30​% of them are blue. The candy company claims that the percentage of blue candies is equal to 25​%. Use a 0.01 significance level to test that claim.

Identify the null and alternative hypotheses for this test. Choose the correct answer below.

Identify the test statistic for this hypothesis test.

The test statistic for this hypothesis test is ?

(Round to two decimal places as needed.)

Identify the p-value for this hypothesis test?

The P-value for this hypothesis test is?

Identify the conclusion for this hypothesis test.

Answer 1

Solution:

This a two- tailed test.

The null and alternative hypothesis is,

Ho: p = 0.25

Ha: p 0.25

Test statistics

z = ( - ) / *(1-) / n

= ( 0.30 - 0.25) / (0.25*0.75) / 100

= 1.16

The test statistic for this hypothesis test is 1.16

P-value = 2 * P(Z > z )

= 2 * ( 1 - P(Z < 1.16 ))

= 2 * 0.1240

= 0.2480

The P-value for this hypothesis test is 0.2480

Since, P-value > 0.01, It is concluded that fail to reject the null hypothesis.