Reference no: EM132409380

1. A simple random sample of 50 calls is monitored at an in-bound call center and the average length of the calls is 6 minutes. The population standard deviation σ is unknown. Instead the sample standard deviation s is also calculated from the sample and is found to be 4 minutes.

a. Construct a 99% confidence interval (using the t-distribution) for the average length of inbound calls.

b. What is the margin of error at the 95% confidence level?

c. Do we need to make any assumption on the distribution of the length of in-bound calls at this call center? Why or why not?

2. According to a previous study, check out times at a supermarket are between 2 to 7 minutes (120 to 8400 seconds) A survey involving a random sample of customers of the supermarket is planned and the first order of business is to decide on an appropriate sample size. The 95% level of confidence will be used.                                                                           

a. What is the planning value for the population standard deviation to be used in the sample size formula for estimating the population mean check-out time?

b. How large should the sample size be if the desired margin of error is 30 seconds?

3. The manager of the Nita-Lake Resort Hotel in Whistle stated that the mean guest bill for a

weekend is $600 or less. A member of the hotel's accounting staff noticed that the total charges for guest bills have been increasing in recent months. the accountant will use a sample of future weekend guest bills to test the manager's claim.                    

a. Which form of the hypotheses should be used to test the manager's claim? Explain.

H_o: µ ≥ 600                H_o: µ ≤ 600                            H_o: µ = 600

H_a: µ < 600                H_a: µ > 600                            H_a: µ ≠ 600

b. What conclusion is appropriate when H_o cannot be rejected?

c. What conclusion is appropriate when H_o can be rejected?

4. In a study entitled How undergraduate Students use credit cards, it was reported that undergraduate students have a mean credit card balance of $3173. This figure was an all-time high and had increased 44% over the previous five years. assume that a current study is being conducted to determine if it can be concluded that the mean credit card balance for undergraduate students has continued to increase compared to the original report. based on previous studies, use a population standard deviation s = $1000.                  

a. State the null and alternative hypotheses.

b. What is the p-value for a sample of 180 undergraduate students with a sample mean credit card balance of $3325?

c. Using a .05 level of significance, what is your conclusion?

5. In a research carried out by an undergraduate student of Yorkville University, six different national brands of chocolate chip cookies were randomly selected at the Superstore supermarket. The grams of fat per serving are as follows: 8; 8; 10; 7; 9; 9. Assume the underlying distribution is approximately normal.

a. Construct a 90% confidence interval for the population mean grams of fat per serving of chocolate chip cookies sold in supermarkets.

i. State the confidence interval.

ii. Sketch the graph.

b. If you wanted a smaller error bound while keeping the same level of confidence, what should have been changed in the study before it was done?

c. Go to the store and record the grams of fat per serving of six brands of chocolate chip cookies.

d. Calculate the mean.

e. Is the mean within the interval you calculated in part a? Did you expect it to be? Why or why not?

6.A national survey of 1,000 adults was conducted on May 13, 2013 by Chrystal Consulting. It concluded with 95% confidence that 49% to 55% of Americans believe that big-time college sports programs corrupt the process of higher education.

a. Find the point estimate and the error bound for this confidence interval.

b. Can we (with 95% confidence) conclude that more than half of all American adults believe this?

c. Use the point estimate from part a and n = 1,000 to calculate a 75% confidence interval for the proportion of American adults that believe that major college sports programs corrupt higher education.

d. Can we (with 75% confidence) conclude that at least half of all American adults believe this?