Problem 1
On the TV show Deal or No Deal, a contestant chooses from among 26 suitcases, each containing a dollar amount. These dollar amounts are:
(a) (2) Using only the table, determine the median prize amount.
(b) (3) Without doing any calculations, how do you expect the mean to compare to the median prize amount? Explain.
(c) (2) Use technology to compute the mean of the prize amounts. In order to calculate the mean I added up each of the 26 numbers together and then divided by 26 to come up with the average per suitcase.
(d) (2) Did your calculation confirm your prediction from part (b)? Are the mean and median close to each other? Explain why this makes sense.
(e)(3) How many and what proportion of the prize amounts are greater than the mean?
(f) (2) How many and what proportion of the prize amounts are greater than the median?
(g) (2) If the producers of the show want to advertise either the mean or median prize amount in order to give the impression that contestants win huge amounts of money, which (mean or median) should they advertise. Explain.
Problem 2
A mother recorded both the age (in months) and height (in cm) of her child during the first few years of her child's life. Shown below is a scatterplot of a few of the recorded data, along with a least-squares regression equation and coefficient of determination. Use this information to answer the following questions.
(2) Even without the data, it is possible to determine the numerical value of the linear correlation coefficient. What is the value? Show all work.
(2) Would the numerical value of the linear correlation coefficient change if the mother had measured her child's height in inches rather than in centimeters? Explain.
(2) Use the least-squares regression line to predict the height of the child at an age of 42 months. Show all work.
(4) Use the least-squares regression line to predicted the height of the child at an age of 30 years old. Does your answer make sense? Why or why not? Show all work.
Problem 3
A big concern that employers have about the use of technology is the amount of time that employees spend each day making personal use of company technology, such as personal phone calls, non-business-related email, Internet use, computer games, etc. A recent study indicated that the average personal-use time of company technology is 75 minutes.
Suppose that the CEO of a large corporation wants to determine whether the average amount of time spent on personal use of company technology for her employees is different from 75 minutes. Each person in a random sample of 10 employees was contacted and asked about daily personal (in minutes) use of company technology. The resulting data are shown in the following table:
(3) What is a specific glaring issue with the data collection that might lead to "non-trustable" results?
(4) Construct a 95% confidence interval for the average time that the CEO's employees use company technology for personal use. Round answers to one decimal place, and show all work.
(3) Using your result to part (b), make a decision about the company CEO's hypothesis regarding her employees' use of company technology for personal use.
Problem 4
Some people seem to believe that you can fix anything with duct tape. In fact, there are people who actually use duct tape to remove warts! A research project was set up to compare the effectiveness of wart removal using duct tape or liquid nitrogen freezing (the routine treatment used by doctors). Patients with warts were randomly assigned to either a duct tape treatment or the freezing treatment. Those in the duct tape group wore duct tape over the wart for 6 days, then removed the tape, soaked the area in water, and used an emery board to scrape the area. This process was repeated for a maximum of 2 months or until the wart was gone. Resulting experiment data are provided.
(2) Which two-sample test should you use for this situation?
(12) Is there sufficient evidence to support the claim that liquid nitrogen freezing is less successful than duct tape in removing warts? Use a significance level of α=0.05. You must state the hypotheses (2 points), determine the test statistic (4 points), and compute either the P-value(s) or critical value(s) (3 points). Finally, you must clearly state your conclusion (3 points). Round all answers to two decimal places.