# Hypothesis testing problems

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1- 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?

2- 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.

3- 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.

#### Solution Summary

Step by step method for testing the hypothesis (ANOVA , t ,F ..) under 5 step approach is discussed here.