Suppose that in a random selection of 100 colored candies, of them are blue. The candy company claims that the percentage of blue candies is equal to . Use a 0.10 significance level to test that claim.
Identify the null and alternative hypotheses for this test. Choose the correct answer below.
A.

C.

D.

Identify the test statistic for this hypothesis test.
The test statistic for this hypothesis test is
(Round to two decimal places as needed.)

Ask by Mejia Norris. in the United States

Mar 21,2025

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 $$ 30 \% $$. Use a 0.10 significance level to test that claim. Identify the null and alternative hypotheses for this test. Choose the correct answer below. A. $$ \mathrm{H}_{0}: \mathrm{p}=03 $$ $$ \mathrm{H}_{1} \mathrm{p}>0.3 $$ $$ \mathrm{H}_{0} \mathrm{p}=0.3 $$ $$ \mathrm{H}_{1} \mathrm{p} 
eq 03 $$ C. $$ \mathrm{H}_{0} \mathrm{p} 
eq 03 $$ $$ \mathrm{H}_{1}: \mathrm{p}=03 $$ D. $$ \mathrm{H}_{0} \mathrm{p}=03 $$ $$ \mathrm{H}_{1}: \mathrm{p}<03 $$ Identify the test statistic for this hypothesis test. The test statistic for this hypothesis test is (Round to two decimal places as needed.)

UpStudy AI · Accepted Answer

$$ H_0: p = 0.3 $$  
$$ H_1: p < 0.3 $$

We use a left-tailed test since the observation (24%) is below the claimed proportion (30%).

The test statistic is computed as follows:

$$
z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}
$$

where  
$$\hat{p} = \frac{24}{100} = 0.24$$,  
$$p_0 = 0.3$$,  
$$n = 100$$.

Calculate the standard error:

$$
\text{Standard Error} = \sqrt{\frac{0.3(1-0.3)}{100}} = \sqrt{\frac{0.3 \times 0.7}{100}} = \sqrt{\frac{0.21}{100}} = \sqrt{0.0021} \approx 0.0458
$$

Now compute the test statistic:

$$
z = \frac{0.24 - 0.3}{0.0458} = \frac{-0.06}{0.0458} \approx -1.31
$$
$$ H_0: p = 0.3 $$ $$ H_1: p < 0.3 $$ The test statistic is approximately -1.31.

Upstudy AI Solution

Answer

Solution

Extra Insights

Related Questions

Latest Statistics Questions