Name ______________________Summer, 2022BUSAD 502EXAM 1Rahul A. ParsaThere are three kinds of lies,Lies,Damn Lies,andStatisticsand in that...

Name ______________________

Summer, 2022

BUSAD 502

EXAM 1

Rahul A. Parsa

There are three kinds of lies,

Lies,

Damn Lies,

and

Statistics

and in that order.

1.


Tom and Rachel, reporters for the Lake Wobegon Register, were investigating the costs charged for the treatment of heart failure and shock by hospitals in the Lake Wobegon area which are given in the accompanying excel file.

a.


Construct a histogram. Describe the shape of the data. What are the typical values?

b.


What are the mean, median, and mode for this data. What do they represent?

c.


Calculate Q1 and Q3 for these data. Interpret these values.

d.


Calculate the Standard deviation? Interpret this value.

e.


Calculate coefficient of variation. Interpret this value.

Please help Tom and Rachel write the report on the findings.

2.


Jacob and Cameron are co-owners of King & Fischer Construction Company. They send out bids on a variety of projects. Some (actually 30%) involve a lot of work in preparing bids for projects they are likely to win, while the others are quick calculations sent in even though they feel it is unlikely that their company will win. Given that Jacob and Cameron put a lot of work into the bid, there is an 80% chance they will win the contract. Given that they submit a quick calculation, their chances of winning the contract are 10%.

a.


Draw a tree diagram for this situation.

b.


What is the probability that Jacob and Cameron will win a contract?

c.


Given that they win a contract, what is the conditional probability that they put a lot of work into the bid.

3.


Joshua and Anthony were anxiously watching the stock market. Assume that the stock market closed at 31,000 points today. Tomorrow they expect the market to raise an average of 200 points, with a standard deviation of 115 points. Assume a normal distribution for the stock market changes.

a.


Find the probability that the stock market goes down tomorrow.

b.


Find the probability that the market goes up more than 100 points tomorrow.

c.


What is the probability that the market changes by more than 200 points in either direction.

4.


Kate and Jared work at the Short Horns NIL office. They raise money to buy student-athletes for their men’s football and basketball teams (according to their opposing coach, IamWiner). A typical fundraising telephone call to an alum results in a donation with a mean of $28.63 with a standard deviation of $13.91. You may assume that donations are received independently of one another.

a.


Based on this information, can you find the probability that a single call will result in a donation of more than $40? Why or why not?

b.


Their intern is expected to make 110 donation calls tomorrow. Find the mean and standard deviation of the resulting total donations.

c.


What is the approximate probability distribution of the total donations to be received by the intern in part b tomorrow`w? How do you know?

d.


Find the probability that the intern in part b will generate a total order of more than $3,300 tomorrow?

5.


Kari and Jamie work for Survey Pig corporation. Their recent market survey has shown that people will spend on average $15.48 each for Iowa Pork products next year based on a sample survey of 483 people. The standard deviation of the sample was $2.52. Find the two-sided 95% confidence interval for next year’s mean expenditure per person in the larger population.

6.


Jason and Will surveyed the customers of Survey Pig and to their surprise, find that 42 out of 200 randomly selected customers were not satisfied with the after-sales support and service. Compute the 95% two-sided confidence interval for the percent dissatisfied among all Survey Pig customers.

7.


Blake and Sarah looked at Jason and Will’s survey data. They collected satisfaction scores given by 12 randomly selected customers of Survey Pig:

89, 98, 96, 65, 99, 81, 76, 51, 82, 90, 96, 76

Does the observed average score differ significantly from the target score of 80? Justify your answer. Use

a


=0.05

8.


Tyler’s goal of his marketing campaign is for more than 25% of supermarket shoppers to recognize his brand name. A recent survey by Survey Pig of 150 random shoppers found that 21.3% recognized his brand name. Does this data indicate that less than 25% of supermarket shoppers recognize his product? Identify the appropriate hypothesis and perform the test at a 5% level.

9.





Theresa, the manufacturer of WeCoolU refrigerators buys bolts from two suppliers, and it is very important that the mean widths of the bolts received from both suppliers are equal since they must be used interchangeably. Theresa receives a large shipment of bolts from each supplier and she draws a random sample of 49 bolts from each shipment. She wants to test whether the mean width is the same in both shipments. Suppose Theresa finds that the mean width of the bolts taken from the one shipment is 1.14 inches with a standard deviation of 0.1 inches and that the mean width of the bolts taken from the other shipment is 1.09 inches with a standard deviation of 0.1 inches. Based on this data, should Theresa reject the hypothesis that the mean widths are equal? Use





a





=

0.05

10.


TrentHomeGrocer.com is an online grocery store in the New Amsterdam area that has more than 10,000 customers. The following table reports May 2022 for a shopping list of eight items from TrentHomeGrocer.com and local New Amsterdam supermarkets.

At a 0.05 level of significance, is there evidence of a difference in the average price for products purchased from TrentHomeGrocer.com and New Amsterdam supermarket? Also, report the p-value.