Question

suppose that in a random selection of 100 colored candles, 30% of them are blue. the candy company claims that the percentage of blue candles is equal to 24%. use a 0.01 significance level to test that claim.

c. ( h_0: p
eq 0.24 )
( h_1: p = 0.24 )
d. ( h_0: p = 0.24 )
( h_1: p
eq 0.24 )
identify the test statistic for this hypothesis test.
the test statistic for this hypothesis test is 1.41
(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: Calculate the \(P -\)value for a two - tailed test

The formula for the \(P -\)value in a two - tailed \(z\) - test is \(P=2\times(1 - \Phi(|z|))\), where \(z = 1.41\) and \(\Phi(z)\) is the cumulative distribution function of the standard normal distribution.
First, find \(\Phi(1.41)\). Using a standard normal table or a calculator with a normalcdf function (\(normalcdf(-\infty,1.41)\)), we know that \(\Phi(1.41)\approx0.9207\)

Step2: Calculate the \(P -\)value

Substitute into the formula \(P = 2\times(1 - 0.9207)\)

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Answer:

\(0.159\)