1.A convenience store manager records the purchases of snacks (by type) and soft drinks (by the brands Coke (C), Pepsi (P), and Mountain Dew (M)). The type of soft drink is also noted (regular or diet). The data are shown below.
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.
2.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
3.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
4.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
5.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
6.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?
g. Conduct the hypothesis test using a 0.05 level of confidence. Give a complete summary including conclusions, evidence, and justification.
Part A
7.The proportions of yearly sales across a province in Canada for five popular fruits (apples, oranges, bananas, peaches, and grapefruit, in terms of units sold to each person per year) were found to be 36%, 26%, 21%, 9%, and 8% respectively. A new survey of 1000 shoppers in a city in that province was conducted and the following purchase frequencies were found:
Apples Oranges Bananas Peaches Grapefruit
391 202 275 53 79
Total: 1000
0.391 0.202 0.275 0.053 0.079
a. What are the null and alternate hypothesis for determining if the market shares for the city differ from the market shares for the province. (If possible, express the hypotheses symbolically).
b. What are the expected numbers of accounts within the sample for the payment statuses?
c. Test your null hypotheses to see if the account payments conform to the pattern of previous years. State complete conclusions.
The account payments do not conform to the pattern of previous year. The purchase frequencies were not equal to proportions of previous yearly sales; this years percentages were apples=39%(not 36%),oranges=20%(not26%)bana
Part B
A travel agent randomly sampled individuals in her target market and asked, "Did you use a travel agent to book your last airline flight?" By cross-referencing the answers to this question with the responses to the rest of the questionnaire, the agent obtained data such as that in the following table:
Age Yes No
< 30 15 30
30 to 39 20 42
40 to 49 47 42
50 to 59 36 50
60 or older 45 20
d. State the null and alternative hypotheses to test if there is a relationship between age and use of a travel agent. (If possible, express the hypotheses symbolically).
e. If use of a travel agent is independent of age, how many people under 30 in the sample would you expect to use a travel agent?
f. Conduct a hypothesis test using a .05 level of significance. State complete concluions:
PART A
8.Television advertisers base their investment decisions regarding the promotion of their products and services on demographic information about television viewers. The age of the viewers is a key factor in this process. The following table shows the number of hours that a random sample of individuals watched television during the week. The individuals are grouped according to their ages.
18-24 25-34 35-49 50-64
39 41 44 49
14 40 19 33
15 33 27 33
17 35 36 39
20 21 49 71
a. State the null and alternative hypotheses to be tested to see if there is a difference in the average number of hours per week of television viewing by the four age groups. (If possible, express the hypotheses symbolically).
b. Perform a hypothesis test to see if there is a difference in the average number of hours per week of television viewing by the four age groups. State complete conclusions. Use a level of significance of 0.05.
c. Briefly explain the method you would use to determine which pairs are different, if any.
PART B
Mike is a restaurant owner and has read about the effect that music can have on the amount of time that customers stay at their tables for dinner. To test this effect, Mike made arrangements to play slow-paced music at his establishment on a busy Saturday night and recorded the time that randomly selected tables spent in the restaurant during five months of the year. Mike did the same on subsequent Saturday nights with fast-paced music and no music. The following data show the amount of time, in minutes, for the observed tables.
MONTH NO MUSIC SLOW FAST
January 60 76 64
March 120 128 115
May 98 110 111
August 73 82 70
October 136 138 142
d. Conduct a hypothesis test to see if a difference exists in the amount of time customers stayed at their tables between the different types of music. Give a complete report of your hypothesis test.
e. Conduct a hypothesis test to see if a difference exists in the amount of time customers stayed at their tables between the different months. Give a complete report of your hypothesis test.
f. Briefly explain the method you would use to determine if there is an interaction between type of music and month of the year.