this is an assignment about introductory statistics for economies.

READALL INSTRUCTIONS BEFORE BEGINNING!!!!!!!!

· Show all your work and formulae.

· All hypothesis tests MUST use the five steps. Formulae are necessary in all cases. The conclusions MUST be complete and include the two parts.

·
Keep a copy of this assignment to study from, solutions will be posted.

· Working in groups to discuss answers is encouraged, but students must submit their own work, and must hand in their own copy.

· Late assignments receive a grade of 0. Failure to submit this assignment leads to an FND in the course.

· There is no need to type the assignment.

1

. (15) Consider a sample of nine wait times measured in seconds at a drive through coffee shop. The sample mean is 95 and the sample standard deviation is 23.516. The population mean and standard deviation are 100 and 20 respectively. (1) What is the size of the sampling error in this case?

a. (3) What is the probability that the average wait time would be less than 80 seconds?

b. (3) What is the probability that the average wait time would be more than 109 seconds?

c. (5) What is the probability that the average wait time would be between 90 and 95 seconds?

d. (3) What is the probability that a customer waits more than 65 seconds?

2. (

12

) A company receives 20 faxed orders every two hours

a. (2) What is the probability that it will receive 8 orders in the next hour?

b. (2) What is the probability that an order will be faxed within the next 9 minutes?

c. (3) What is the probability that more than 12 minutes will elapse between faxed orders?

d. (5) The company also receive online orders. These orders are over $200 on average 15% of the time. What is the probability that in a sample of 10 online orders, 5 or 6 will be over $200?

3. (13) The student body of a local college draws 40% of its students from Ontario, 35% from the rest of Canada, and the remainder from outside Canada. Of those from Ontario, 60% are female, of those from the rest of Canada 25% are female, and of those from outside Canada, 15% are female.

a. (3) What is the probability of a male student from Ontario?

b. (5) What is the probability of a female student?

c. (5) What is the probability of a male student who did not come from Ontario?

4. (15) The number of cups of coffee served at a local Tim Horton’s during the morning rush hour between 7 and 9 AM is normally distributed. Based on sales a day is described as SLOW if less than 200 cups are served, AVERAGE 200- 249 cups are sold, and BUSY if over 250 cups are sold during the day. A random sample of five days was taken and the sales figures observed. The sample mean is 208 cups and the sample standard deviation is 25.5734.

a. (6) Construct a 99% confidence interval for the population average sales for this period.

b. (2) Based on your confidence interval, can you conclude the type of day that the average sales would be considered as defining – SLOW, AVERAGE, or BUSY? Explain your conclusion.

c. (6) Management is concerned that the average is falling below the national average of 210 cups per day. Test this hypothesis using alpha = 0.05.

d. (1) What assumption must hold to allow you to construct the confidence interval and test the hypothesis in this case?

5. (19) The life insurance industry maintains that the average worker in Saskatoon has no more than $25,000 of personal life insurance. You believe it is higher. You sample 100 workers in Saskatoon at random and find the sample average to be $26,650 of personal life insurance. The population standard deviation is known to be $12,000. Use α=0.05 throughout.

a. (6) Test your belief using a significance level of 5%.

b. (6) Explain, in the context of this question, what is meant by a Type I error, a Type II error, and the power of the test?

c. (5) If the true average for this population is in fact $30,000, what is the probability of committing a Type II error?

d. (2) Calculate the power of the test.

6. (12) Consider two independent, normally distributed populations whose variances are unknown but thought to be equal. Samples from the two yield the following results:

Group 1

Group 2

Sample Mean

13.46

9.61

Sample standard deviation

3.62

2.89

Sample size

8

8

df = n1

+

n2-2 = 14 AND

a. (6) Test the hypothesis that there is a difference in the population means. Use α = 0.05.

b. (6) Historical data showed that the standard deviation of Group 1 is 3. Does the sample support the belief that the standard deviation has increased. Test that this is still true using alpha = 0.05.

7. (14) A company is reviewing the performance of two different suppliers of toner ink as their intention is to compare them and possibly switch to the alternate one. Using the following data for hours of toner use before empty answer the following.

CURRENT SUPPLIER A

ALTERNATE SUPPLIER B

Mean

501.7

495.3

Variance

102.3

20.1

Observations

20

20

df = n1+n2-2 = 38 AND

a. (6) Determine if the standard deviation of the Alternate Supplier B is significantly less than 5. Use alpha = 0.05.

b. (6) Assuming that the variances of the two are not equal, test to determine if the Current Supplier A has more than 2 hours average hours of toner use than Alternate Supplier B. Use alpha = 0.05.

c. (2) What is your recommendation to the company with respect to the supplier to select? Explain.

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