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. Find the sample mean and sample standard deviation of the amount citizens spend per year.
2. When finding a confidence interval for the true mean spent of ALL citizens, should we use a z-score or a t-score? Why?
3. Find the z/t-values (as appropriate) for a 95% confidence interval and a 92% confidence interval.
4. Find a 95% and a 92% confidence interval for the true mean amount that citizens spend per year.
5. What do you think the lowest possible mean amount spent per year is? Why?
6. Do you think Bob has a good customer base for his new business? Explain.
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