Assignment:
Q1- At LLD Records, some of the market research of college students is done during promotions on college campuses, while other market research of college students is done through anonymous mail, phone, internet, and record store questionnaires. In all cases, for each new CD the company solicits an "intent-to-purchase" score from the student, with being the lowest score ("no intent to purchase") and being the highest score ("full intent to purchase").
The manager finds the following information for intent-to-purchase scores for a soon-to-be-released CD
Group Sample size Sample Mean Sample variance
On campus 23 69.3 86.3
By mail 23 63.7 45
By phone 23 58.9 99.8
By internet 23 61.7 41.1
In a store 23 61 106.4
The manager's next step is to conduct a one-way, independent-samples ANOVA test to decide if there is a difference in the mean intent-to-purchase score for this CD depending on the method of collecting the scores.
Answer the following, carrying your intermediate computations to at least three decimal places and rounding your responses to at least one decimal place.
a- What's the value of the mean square for error (the "within groups" mean square) that would be reported in the ANOVA test?
b- What's the value of the mean square for treatment (the "within groups" mean square) that would be reported in the ANOVA test?
Q2- In an effort to counteract student cheating, the professor of a large class created four versions of a midterm exam, distributing the four versions among the students in the class, so that each version was given to students. After the exam, the professor computed the following information about the scores (the exam was worth points):
Group Sample size Sample Mean Sample variance
Version A 75 159.5 270.3
Version B 75 153 331.6
Version C 75 157.5 365.6
Version D 75 153.7 331.4
The professor is willing to assume that the populations of scores from which the above samples were drawn are approximately normally distributed and that each has the same mean and the same variance.
Answer the following, carrying your intermediate computations to at least three decimal places and rounding your responses to at least one decimal place.
a- give an estimate of this common population variance by pooling the sample variances given.
b- give an estimate of this common population variance by pooling the sample means given.
Q3- Emma's On-the-Go, a large convenience store that makes a good deal of money from magazine sales, has three possible locations in the store for its magazine rack: in the front of the store (to attract "impulse buying" by all customers), on the left-hand side of the store (to attract teenagers who are on that side of the store looking at the candy and soda), and in the back of the store (to attract the adults searching through the alcohol cases). The manager at Emma's experiments over the course of several months by rotating the magazine rack among the three locations, choosing a sample of days at each location. Each day, the manager records the amount of money brought in from the sale of magazines.
Below are the sample mean daily sales (in dollars) for each of the locations, as well as the sample variances:
Group Sample size Sample Mean Sample variance
Front 44 212.1 454.9
Left-hand side 44 219.7 295.4
Right-hand side 44 219 417.1
Suppose that we were to perform a one-way, independent-samples ANOVA test to decide if there is a significant difference in the mean daily sales among the three locations.
Answer the following, carrying your intermediate computations to at least three decimal places and rounding your responses to at least one decimal place.
a- What's the value of the mean square for error (the "within groups" mean square) that would be reported in the ANOVA test.
b- What's the value of the mean square for treatment (the "within groups" mean square) that would be reported in the ANOVA test.
Q4- Jointsoft is a great over-the-counter arthritis medication, but who will ever know about it? Unfortunately, many people with arthritis tend to be elderly and rather immobile, so advertisers of arthritis medications face limitations in ways to get their messages across. Currently, their best modes of advertisement are commercials on daytime TV, advertisements in select magazines, fliers in convalescent homes, and (believe it or not) advertisements on certain Web pages.
Marketing managers for Jointsoft are investigating these four modes of advertisement in four small communities (with a different mode of advertisement in each community). The marketing managers have selected days at random and are looking at the daily sales (in dollars) in each of the communities on each of these days. Here is what they have to work with
Group Sample size Sample Mean Sample variance
TV 33 566.5 2937.4
Magazines 33 567.8 2789.2
Fliers 33 570 1389.6
Web pages 33 602 3793
Suppose that the marketing managers perform a one-way, independent-samples ANOVA test to decide if there are differences in the mean daily sales arising from the four modes of advertisement. (So, they're assuming that the only difference among the four communities is the mode of advertisement used in it.) Such a test uses the statistic
Variation between the samples .
Variation within the samples
For the information in the chart above,
a- Give the P value corresponding to this value F statistic. Round your answer to at least 3 decimal places.
b- Using the 0.01 level of significance, can the marketing managers conclude that the mean daily sales arising from at least one of the modes of advertising differs from the others?
Q5- The General Social Survey is an annual survey given to a random selection of about adults in the United States. Among the many questions asked are "What is the highest level of education you've completed?" and "If you're employed full-time, how many hours do you spend working at your job during a typical week?"
In a recent year, respondents answered both questions. The summary statistics are given in the chart below. (The sample data consist of the times, in hours per week, that were given by the respondents.)
Group Sample size Sample Mean Sample variance
less than h.s 291 42 93.8
high school 295 42.9 100.6
bachelor's 300 43.9 91.8
graduate 285 41.4 92.2
To decide if there are any differences in the mean hours per week worked by these different groups, we can perform a one-way, independent-samples ANOVA test. Such a test uses the statistic
Variation between the samples .
Variation within the samples
For the data from the survey,
a- Give the numerator degrees of freedom of this F statistic
b- Give the denominator degrees of freedom of this F statistic
c- From the survey data, can we conclude that at least one of the groups differs significantly from the others in mean hours worked in a typical week? Use the level of significance 0.10
Q6- Cris Turlock owns and manages a small business in San Francisco, California. The business provides breakfast and brunch food, via carts parked along sidewalks, to people in the business district of the city.
Being an experienced businessperson, Cris provides incentives for the four salespeople operating the food carts. This year, she plans to offer monetary bonuses to her salespeople based on their individual mean daily sales. Below is a chart giving a summary of the information that Cris has to work with. (In the chart, a "sample" is a collection of daily sales figures, in dollars, from this past year for a particular salesperson.
Group Sample size Sample Mean Sample variance
salesperson 1 126 204.6 2104.8
salesperson 2 113 216.5 2553.2
salesperson 3 73 217.8 2445.1
salesperson 4 124 225.2 2411.4
Cris' first step is to decide if there are any significant differences in the mean daily sales of her salespeople. (If there are no significant differences, she'll split the bonus equally among the four of them.) To make this decision, Cris will do a one-way, independent-samples ANOVA test of equality of the population means, which uses the statistic
Variation between the samples .
Variation within the samples
For these samples, .
a- Give the P value corresponding to this F value statistic. Round to at least 3 decimal points
b- Can we conclude, that at 0.05 level of significance, that at least one of the salesperson is significantly different from the others?