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Solve: Hypothesis Testing and Confidence Intervals

Bob's Candies

Bob loves making candy, especially varieties of caramel, including plain, chocolate dipped caramels and chocolate dipped caramels with pecans. Bob has received lots of compliments from his friends and neighbors, and several have encouraged him to start his own candy making business.

After several days of research, Bob finds that the national average amount of money spent annually per person on this type of specialty candy is $75. Bob believes that the citizens in his area spend more than that per year. Knowing whether or not this is true could help Bob make a wise decision regarding his future business plans.

Bob wants to use statistics to support his claim, and to help him obtain a small business loan. Bob also wants to find an estimate of the true amount of money local citizens do spend on this type of specialty candy.

Bob randomly selects several people from his local phone book and asks the person that answers how much money they typically spend per year on candy like he will make. He obtains the following results (in dollars): 75, 74, 80, 68, 79, 85, 77, 82, 79, 67, 90, 72, 76, 75, 69, 85, 78, 79, 82, 66, 75, 85, 90, 76, 85, 67, 89, 82, 69, 79, 82, 80, 84, 79, 78, 81, 77, 84, 80, 76.

Based upon these results, Bob is hoping his area has a good customer base for his new business. Bob also hopes the bank is impressed with his use of statistics and will grant him the loan he needs to start it.

1. What is an appropriate set of hypothesis for Bob to test?
2. Is a z- or t-value test appropriate for this situation? Why?
3. Perform an appropriate hypothesis test, showing all critical steps.
4. Do you support Bob's claim that citizens in his area spend more than $75 per year? Explain why or why not.
5. Find a 95% confidence interval for the true mean amount that citizens spend per year.
6. What do you think the lowest possible mean amount spent per year is? Why?
7. Does your answer to 6 agree with your answer to 4? Explain.
8. Do you think Bob has a good customer base for his new business? Explain.

Solution Preview

Please see attached file for a fully formatted explanation.
Please view the attached file for a fully formatted solution which illustrates how the values have been calculated.

Null Hypothesis: Amount spent by the citizens per year on this type of candy = $75.
Alternate Hypothesis: Amount spent by the citizens on this type of candy more than $75.

To test the above hypothesis, we use Z-statistic test, because the sample size is 40 (which is greater than 30).
If the sample size would have been less than 30, we would use t-statistic ...

Solution Summary

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