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): (The proportion of red candies is equal to 20%, as claimed by the company.)
Alternative hypothesis (H₁): (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:
- What is the significance level in hypothesis testing?
- How do you calculate a p-value for a hypothesis test?
- What are Type I and Type II errors in hypothesis testing?
- How can Jackson collect data for his hypothesis test on red candies?
- 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
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