Question

suppose that in a random selection of 100 colored candies, 24% of them are blue. the candy company claims that the percentage of blue candies is equal to 27%. use a 0.05 significance level to test that claim.

d. ( h_{0}: p = 0.27 )
( h_{1}: p>0.27 )
identify the test statistic for this hypothesis test.
the test statistic for this hypothesis test is - 0.68.
(round to two decimal places as needed.)
identify the p - value for this hypothesis test.
the p - value for this hypothesis test is (square).
(round to three decimal places as needed.)

Explanation:

Step1: Determine the type of test

Since \(H_1: p>0.27\), this is a right - tailed test.

Step2: Calculate the P - value

For a right - tailed z - test, the P - value is \(P(Z>z)\), where \(z=- 0.68\).
Using the property \(P(Z > z)=1 - P(Z\leq z)\)
From the standard normal table, \(P(Z\leq - 0.68)=0.2483\)
So \(P(Z>-0.68)=1 - 0.2483 = 0.7517\approx0.752\)

Answer:

The P - value for this hypothesis test is \(0.752\)