Math Problem Statement

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

Solution

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=0.20p = 0.20 (The proportion of red candies is equal to 20%, as claimed by the company.)

Alternative hypothesis (H₁): p0.20p \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


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!

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Math Problem Analysis

Mathematical Concepts

Hypothesis Testing
Proportions
Statistics

Formulas

p̂ = x/n (sample proportion)
Null hypothesis: p = 0.20
Alternative hypothesis: p ≠ 0.20

Theorems

Central Limit Theorem
Hypothesis Testing for Proportions

Suitable Grade Level

Grades 10-12