MATH 221 Week 8 Page 2 Answers

1. (TCO 8) For the following statement, write the null hypothesis and the alternative hypothesis. Also label which one is the claim.
A car manufacturer claims that their cars makes at least 35 miles per gallon of fuel. (Points: 8)

2. (TCO 11) A pizza restaurant manager claims that the average home delivery time for their pizza is no more than 20 minutes. A random sample of 49 home delivery pizzas was collected. The sample mean was found to be 21.25 minutes and the standard deviation was found to be 4.3 minutes. Is there evidence to reject the manager’s claim at alpha =.01? Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results. (Points: 20)

3. (TCO 5) A multiple choice exam contains 50 questions. Each question has 5 choices, one of which is correct. We are interested in knowing the probability guessing exactly 18 questions correctly.

(a) Is this a binomial experiment? Explain how you know.

(b) Use the correct formula to find the probability of guessing exactly 18 questions correctly out of the 50 questions. Show your calculations or explain how you found the probability. (Points: 20)

4. (TCO 6) The monthly utility bills are normally distributed with a mean value of $150 and a standard deviation of $20.

(a) Find the probability of having a utility bill between 135 and 170.

(b) Find the probability of having a utility bill less than $135.

 (c) Find the probability of having a utility bill more than $180. (Points: 20)

5. (TCO 8) A Mall manager claims that in average every customer spends $52 per a single visit to the mall. To test this claim, you took a sample of 36 customers and found the sample mean to be $55 and the sample standard deviation to be $12. At alpha = 0.05, test the Mall’s manager claim. Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results. (Points: 20)

6. (TCO 7) A bank manager wanted to estimate the mean number of transactions businesses make per month. For a sample of 60 businesses, he found the mean number of transaction per month to be 38 and the standard deviation to be 8.5 transactions.

(a) Find a 95% confidence interval for the mean number of business transactions per month. Show your calculations and/or explain the process used to obtain the interval.

(b) Interpret this confidence interval and write a sentence that explains it. (Points: 20)

7. (TCO 7) A company’s CEO wanted to estimate the percentage of defective product per shipment. In a sample containing 400 products, he found 25 defective products.

(a) Find a 95% confidence interval for the true proportion of defective product. Show your calculations and/or explain the process used to obtain the interval.

(b) Interpret this confidence interval and write a sentence that explains it. (Points: 20)

8. (TCO 2) The ages of 10 students are listed in years:

 { 17,22,19,24,21,23,29,18,22,28 } (Points: 20)

(a) Find the mean, median, mode, sample variance, and range.

(b) Do you think that this sample might have come from a normal population? Why or why not? (Points: 20)