Jackson wants to test an assumption on the number of red candies in a bag of Fruity Tooty's candy. The company claims that five flavors are given an equal distribution in each bag, meaning that the proportion of each color should be 20%. Jackson decides to focus his efforts on examining whether there is a difference in the proportion of red candies than what the company claims.

What should Jackson state for the null hypothesis and alternative hypothesis?


A.)
Null hypothesis: p equals 0.20
Alternative hypothesis: p not equal to 0.20


B.)
Null hypothesis: p greater than 0.20
Alternative hypothesis: p less than 0.20


C.)
Null hypothesis: p not equal to 0.20
Alternative hypothesis: p equals 0.20


D.)
Null hypothesis: p equals 0.20
Alternative hypothesis: p greater than 0.20

Jackson's goal is to test whether the proportion of red candies is different from the company's claimed proportion of 20%. Therefore, he is testing if the actual proportion is equal to 0.20 or if it is different from 0.20.

- The **null hypothesis** represents the statement being tested, usually assuming no difference or status quo (in this case, the company's claim that the proportion is 20%).
- The **alternative hypothesis** represents a deviation from this status quo (in this case, Jackson's question whether the proportion of red candies is different from 20%).

The correct formulation would be:

**Null hypothesis (H₀)**: \( p = 0.20 \) (The proportion of red candies is equal to 20%, as claimed by the company.)

**Alternative hypothesis (H₁)**: \( p \neq 0.20 \) (The proportion of red candies is different from 20%.)

Thus, the correct answer is:

**A.) Null hypothesis: p equals 0.20; Alternative hypothesis: p not equal to 0.20**

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Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. What is the significance level in hypothesis testing?
2. How do you calculate a p-value for a hypothesis test?
3. What are Type I and Type II errors in hypothesis testing?
4. How can Jackson collect data for his hypothesis test on red candies?
5. What are the steps for conducting a hypothesis test for proportions?

**Tip:** Always check the assumptions of your hypothesis test, like sample size and randomness, to ensure valid results!

Jackson wants to test an assumption on the number of red candies in a bag of Fruity Tooty's candy. The company claims that five flavors are given an equal distribution in each bag, meaning that the proportion of each color should be 20%. Jackson decides to focus his efforts on examining whether there is a difference in the proportion of red candies than what the company claims. What should Jackson state for the null hypothesis and alternative hypothesis? A.) Null hypothesis: p equals 0.20 Alternative hypothesis: p not equal to 0.20 B.) Null hypothesis: p greater than 0.20 Alternative hypothesis: p less than 0.20 C.) Null hypothesis: p not equal to 0.20 Alternative hypothesis: p equals 0.20 D.) Null hypothesis: p equals 0.20 Alternative hypothesis: p greater than 0.20

Test a claim about the proportion of red candies in Fruity Tooty's candy bags. The company claims the proportion is 20%, and Jackson is testing whether it differs. This problem involves hypothesis testing for proportions, key statistical concepts, and step-by-step guidance. Suitable for Grades 10-12 students.

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