Question

suppose that in a random selection of 100 colored candles, 24% of them are blue. the candy company claims that the percentage of blue candies is equal to 30%. use a 0.01 significance level to test that claim. identify the null and alternative hypotheses for this test. choose the correct answer below. a. $h_{0}:p = 0.3$ $h_{1}:p
eq0.3$ b. $h_{0}:p = 0.3$ $h_{1}:plt0.3$ c. $h_{0}:p = 0.3$ $h_{1}:pgt0.3$ d. $h_{0}:p
eq0.3$ $h_{1}:p = 0.3$ identify the test statistic for this hypothesis test. the test statistic for this hypothesis test is (round to two decimal places as needed.)

Explanation:

Step1: Calculate sample proportion

The sample proportion $\hat{p}$ is given as $0.24$ (since $24\% = 0.24$), the hypothesized proportion $p = 0.3$, and the sample size $n = 100$.

Step2: Compute the test - statistic formula

The formula for the test - statistic $z$ in a proportion test is $z=\frac{\hat{p}-p}{\sqrt{\frac{p(1 - p)}{n}}}$.
Substitute the values: $\hat{p}=0.24$, $p = 0.3$, $n = 100$.
First, calculate the denominator: $\sqrt{\frac{0.3\times(1 - 0.3)}{100}}=\sqrt{\frac{0.3\times0.7}{100}}=\sqrt{\frac{0.21}{100}}=\sqrt{0.0021}\approx0.0458$.
Then, calculate the numerator: $0.24 - 0.3=- 0.06$.
Now, find $z$: $z=\frac{-0.06}{0.0458}\approx - 1.31$.

Answer:

The test statistic for this hypothesis test is $-1.31$.