Question

suppose that in a random selection of 100 colored candies, 22% of them are blue. the candy company claims that the percentage of blue candies is equal to 23%. use a 0.10 significance level to test that claim.

b. ( h_{0}: p = 0.23 )
( h_{1}: p < 0.23 )
c. ( h_{0}: p
eq 0.23 )
( h_{1}: p = 0.23 )
d. ( h_{0}: p = 0.23 )
( h_{1}: p
eq 0.23 )
identify the test statistic for this hypothesis test.
the test statistic for this hypothesis test is - 0.24
(round to two decimal places as needed.)
identify the p - value for this hypothesis test.
the p - value for this hypothesis test is
(round to three decimal places as needed.)

Explanation:

Step1: Determine the type of test

Since \(H_1: p
eq0.23\), this is a two - tailed test.

Step2: Use the formula for the P - value in a two - tailed z - test

The formula for the P - value in a two - tailed z - test is \(P - value = 2\times(1 - \Phi(|z|))\), where \(z=- 0.24\) and \(\Phi\) is the cumulative distribution function of the standard normal distribution.
First, find \(\Phi(0.24)\). Looking up in the standard normal table or using a calculator with a normalcdf function (\(normalcdf(-\infty,0.24)\)), we know that \(\Phi(0.24)\approx0.5948\)
Then calculate \(P - value=2\times(1 - 0.5948)\)

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Answer:

\(0.810\)