Suppose that in a random selection of

100
 
colored​ candies,

27

​% 

of them are blue. The candy company claims that the percentage of blue candies is equal to

28

​%. 

Use a

0.05
 
significance level to test that claim.

Question content area bottom

Part 1

Identify the null and alternative hypotheses for this test. Choose the correct answer below.

To test the claim that the percentage of blue candies is equal to 28%, we need to set up the null hypothesis (\( H_0 \)) and the alternative hypothesis (\( H_a \)).

Here’s how the hypotheses are structured:

- **Null Hypothesis (\( H_0 \))**: The candy company's claim is correct, so the percentage of blue candies is 28%. In statistical terms, this is:
  \[
  H_0: p = 0.28
  \]
  
- **Alternative Hypothesis (\( H_a \))**: The percentage of blue candies is not 28%. This is a two-tailed test because we are testing whether the true percentage differs from 28% in either direction. In statistical terms, this is:
  \[
  H_a: p \neq 0.28
  \]

### Answer:
The correct hypotheses are:
- \( H_0: p = 0.28 \)
- \( H_a: p \neq 0.28 \)

Do you want more details on the steps for conducting the test? Here are some follow-up questions to expand on this:

1. What is the test statistic used to perform this hypothesis test?
2. How do we calculate the sample proportion for this test?
3. How do we determine the critical value for a 0.05 significance level?
4. What is the conclusion if the test statistic falls within the critical region?
5. How do we interpret a p-value in the context of hypothesis testing?

**Tip:** Always clearly define your null and alternative hypotheses before conducting any statistical test.

Suppose that in a random selection of 100 colored candies, 27% of them are blue. The candy company claims that the percentage of blue candies is equal to 28%. Use a 0.05 significance level to test that claim.

Learn how to perform a hypothesis test to check the candy company's claim that 28% of their candies are blue. We use a significance level of 0.05 to test whether the true proportion differs from the company's claim. Understand the steps involved, including calculating the test statistic and interpreting the results.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation