a. Would you consider these data to be sample data or population data? Explain and justify your answer.
b. How many observations are in these data?
c. How many variables are in these data?
d. What is the measure of central tendency for the Brand? Give both the measure and its value:
measure: value:
e. Construct a frequency distribution for the Brand of soda.
f. Construct an appopriate graphical representation of the distribution from part e.
g. Give a comment about something that can be learned from the data based on either your answer in part e or part f.
h. Create a crosstabulation showing both Brand and Type of soda.
i. Give a comment about something that can be learned about both the brand and type of soft drink purchases from the crosstabulation in part h.
j. Is the choice of Pepsi independent of the choice of Diet? Give complete evidence for your answer.
A survey of a sample of 200 executives attending a conference yielded the following information regarding the type of industry and their geographic location:
Communications Toronto Calgary Vancouver Montreal Total
Finance 24 10 8 14 56
Manufacturing 30 6 22 12 70
Communications 28 18 12 16 74
Total 82 34 42 42 200
a. Using these data, construct a joint probability table in the space below:
Communications Toronto Calgary Vancouver Montreal Total
Finance 0.12 0.05 0.04 0.07 0.28
Manufacturing 0.15 0.03 0.11 0.06 0.35
Communications 0.14 0.09 0.06 0.08 0.37
Total 0.41 0.17 0.21 0.21 1
b. What percentage of executives in the sample work in Finance?
c. What is the probability of selecting an individual who is from Calgary or Vancouver?
d. What is the probability of selecting an individual who is from Montreal and works in Communications?
e. What is the probability of selecting an executive who works in Manufacturing given that the person is from Toronto?
PART B
Kate and Wally each lead a team of sales representatives in the same company. The data below show their teams' sales over the last year.
f. Compute the table below for both Kate and Wally's teams.
g. Based on the first 3 measures from the table in part f, who would you say has the better sales team? Be sure to explain and justify your answer.
h. Based on the highest and lowest sales measures from the table in part f, who would you say has the better sales team? Be sure to explain and justify your answer. i. Based on the standard deviations from part f, who would you say has the better sales team? Be sure to explain and justify your answer.
PART A
According to a survey, 60% of all consumers have called an information line concerning a product. Suppose a random survey of 25 consumers is contacted and interviewed about their buying habits.
a. What is the probability that 15 or more of these consumers have called an information line concerning a product?
b. What is the probability that more than 20 of these consumers have called an information line concerning a product?
c. What is the probability that fewer than 10 of these consumers have called an information line concerning a product?
PART B
The manager of a computer store has kept track of the number of computers sold per day. On the basis of this information, the manager produced the following list of the number of daily sales.d. What is the expected number of sales per day?
e. What is the probability of selling at least 3 computers in a day?
f. What is the probability of no sales in a day?
PART C
A bank has an average random arrival rate of 3.2 customers every 4 minutes.
g. What is the probability of getting exactly 10 customers during an 8-minute interval?
h. What is the probability that at least 4 customers will enter the bank during a 4-minute interval?
PART A
For the 900 trading days from January 2003 through July 2006, the daily closing price of IBM stock (in $) is well modelled by a Normal distribution with mean $85.60 and standard deviation $6.20. According to this model, what is the probability that on a randomly selected day in this period the stock price closed:
MEAN 85.6 ST.DEV. 6.2
a. above $91.80?
b. below $98?
c. between $73.20 and $98?
d. Above what price does the stock close on 80% of days?
PART B
The amount of time a bank teller spends with each customer is expected to be normally distributed with a population mean of 3.10 minutes and standard deviation of 0.40. If you select a random sample of 16 customers:
e. below how many minutes would you expect 90% of the sample means to be?
f. what is the probability that the sample mean is less than 3 minutes?
g. what is the probability that the sample mean time spent per customer is greater than 3.5 minutes?
h. if the sample mean time is found to be 3.5 minutes, what might you conclude about the population mean? Explain and justify your answer.
PART A
When considering various carbon tax options, the Ministry of Transportation wants to know what the average gasoline consumption per car in Canada is. The data below represent the number of litres used per day for 25 randomly selected cars.
a. Based on the data, what might they estimate the average daily gas consumption per car to be?
b. With 95% confidence, within what range is the daily average gas consumption per car?c. One policy that is being considered is based on the assumption that the average daily gas consumption per car is 6 litres. Based on your answer in part b, would it be reasonable for the Ministry to consider this policy? Explain your answer.
PART B
Prior to the release of the iPhone 4 during the summer of 2010, Apple had a 24% share of the smart phone market. Suppose Apple believed that the release of the iPhone 4 would increase the company's market share. To test this hypothesis, after the phone was released, a random sample of 275 smart phone users was selected, 82 of whom owned iPhones. A level of significance of 0.05 is required.
d. Determine the point estimate for the market share following the iPhone 4 release.
e. Indicate what the hypotheses would be for determining whether the market share for iPhone has increased.
f. What test statistic would you need to calculate to test this hypothesis? What is its value?
g. For the hypothesis test, specify EITHER the p-value OR the critical value:
h. Complete the hypothesis test and state complete conclusions:
i. Explain what type of error you could have made in this hypothesis test?
PART A
Office occupancy in a city is an indication of the economic health of the region in which it is located. A random sample of offices in Vancouver and Toronto was selected, and the number of vacancies was recorded. The data are as follows:
Toronto Vancouver
Number of vacancies: 24 17 pro. Vancouver 0.467741935
Number in sample: 165 145 pro.-toronto 0.532258065
a. If D is defined as pToronto - pVancouver, what is the point estimate for D?
b. What are the hypotheses that would be used to test if there is a difference in the vacancy rates in the two cities?
c. What are the hypotheses that would be used to test if the vacancy rates is greater in Toronto?
PART B
McDonald's would like to compare the wait times its drive-through customers experience vs. the wait times its customers using the restaurants' inside counters experience. The data below represent the wait times, in minutes, randomly selected customers in the two types of groups experienced.
d. State the hypotheses that will be used to test the claim that the drive-throughs offer faster service than at the inside counters.
e. Is this an upper, lower, or two-tailed test?
f. What type of test would be used to for this hypothesis test?