A marketing consultant was hired to visit a random sample of five sporting goods stores across the state of California. Each store was part of a large franchise of sporting goods stores. The consultant taught the managers of each store better ways to advertise and display their goods. The net sales for 1 month before and 1 month after the consultant’s visit were recorded as follows for each store (in thousands of dollars):

Before visit: 57.1 94.6 49.2 77.4 43.2
After visit: 63.5 101.8 57.8 81.2 41.9

use a 1% level of significance

a. State the null and alternative hypotheses ?0: ?1:

b. What calculator test will you use? List the requirements that must be met to use this test, and indicate whether the conditions are met in this problem.

c. Run the calculator test and obtain the P-value.

d. Based on your P-value, will you reject or fail to reject the null hypothesis?

e. Interpret your conclusion from part d in the context of this problem

A nightclub manager realizes that demand for drinks is more elastic among students, and is
trying to determine the optimal pricing schedule. Specifically, he estimates the following average
demands:
• Under 25: qr = 18 − 5p
• Over 25: q = 10 − 2p
The two age groups visit the nightclub in equal numbers on average. Assume that drinks cost the
nightclub $2 each.

(d) Now suppose that it is impossible to distinguish between types. If the nightclub lowered
drink prices to $2 and still wanted to attract both types of consumer, what cover charge would
it set?
(e) Suppose that the nightclub again restricts itself to linear pricing. While it is impossible to
explicitly “age discriminate,” the manager notices that everyone remaining after midnight
is a student, while only a fraction 2/7
of those who arrive before midnight are students. How
should drink prices be set before and after midnight? What type of price discrimination is
this? Compare profits in (d) and (e).

[6 marks]

A researcher was interested in finding out whether Moral Reasoning could be enhanced if students were taught using Moral Dilemmas. Subjects were given a Moral Reasoning Test before the treatment (using moral dilemmas) and after the treatment and the results are shown in Table 1 below.

1. Describe the findings in Table 1
2. State the null hypothesis
3. State the alternative hypothesis
4. Why is the paired t-test used? [as shown in Table 2 above]
5. What can you conclude from Table 2?

Two cars start from rest at a red stop light. When the light turns green, both cars accelerate forward. The blue car accelerates uniformly at a rate of 4.7 m/s² for 3.8 seconds. It then continues at a constant speed for 8.7 seconds, before applying the brakes such that the car’s speed decreases uniformly coming to rest 212 meters from where it started. The yellow car accelerates uniformly for the entire distance, finally catching the blue car just as the blue car comes to a stop.

1. How fast is the blue car going 2.7 seconds after it starts?

2. How fast is the blue car going 10.2 seconds after it starts?

3. How far does the blue car travel before its brakes are applied to slow down?

4. What is the acceleration of the blue car once the brakes are applied?

5. What is the total time the blue car is moving?

6. What is the acceleration of the yellow car?

Find solutions to the following problems. Use the appropriate t-test to test for significant mean differences in the following research scenarios. Report all relevant information, including hypotheses, degrees of freedom, critical value, and a statement about significance.

A researcher wants to see if antihistamines will increase the amount of time in seconds it takes participants to react to a surprise stimulus. He first collects the participants' reaction times while not on antihistamines, and then gives them the dose of antihistamine. One hour later, he collects the participants' reaction times again. Participant ID Reaction Time Before Antihistamine Reaction Time After Antihistamine

A simple random sample of 100 adults is obtained, and each person’s red blood cell count (in cells per microliter) is measured. The sample mean is 5.22 and the sample standard deviation is 0.53. Use a 0.01 significance level to test the claim that the sample is from a population with a mean less than 5.3, the calculated value of t-test statistic is (Given that H0: µ = 5.3, Ha:µ < 5.3)

choose

-15.09

15.09

-1.509

1.509

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Three students took a statistics test before and after coaching, but coaching did not effect the scores of students i.e mean change in scores is zero. Their scores are as follows:

The value of t-test statistic for matched pairs is

choose

8.66

0.866

-0.866

-8.66

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The basic procedure of hypothesis testing is to make an initial assumption about the population parameter, collect evidence and decide whether to "reject" or "not reject" our initial assumption.

choose

True

False

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i)What test would you do to find out if Drug A is effective?

a)when data follows normal distribution

b)when data does not follow normal distribution, provide two methods to find out if the drug Is effective; how is one advantageous over the other method?

A company that makes shopping carts for supermarkets and other stores recently purchased some new equipment that reduces the labour content of the jobs needed to pro- duce the shopping carts. Prior to buying the new equip- ment, the company used four workers, who produced an average of 80 carts per hour. Labour cost was $10 per hour and machine cost was $40 per hour. With the new equipment, it was possible to transfer one of the workers to another department. Machine cost increased by $10 per hour while output increased by four carts per hour.

a. Calculate labour productivity before and after the new equipment. Use carts per worker per hour as the meas- ure of labour productivity.

b. Calculate the multi-factor productivity before and after the new equipment. Use carts per dollar cost (labour plus machine) as the measure.

c. Comment on the changes in productivity according to the two measures. Which one do you believe is more pertinent for this situation?

1. The concept of mutual assent is also called a/an: ___ Agreement of sorts. ___ Meeting of the minds. ___ Intent to negotiate. ___ Void contract. ___ Contract in rem.

2. If the offeror revokes her offer before acceptance by the offeror, the offer is: ___ Terminated, by operation of law. ___ Terminated, by action of the parties. ___ Not terminated, because all offers are irrevocable. ___ None of the above.

3. The mailbox rule determines the effective date of the: ___ Acceptance ___ Revocation ___ Rejection ___ Postmark ___ Mutual assent

4. The night before his commencement ceremony, Leland’s uncle promises to buy him a new car after he actually sees Leland receive his diploma. Leland gladly accepts. After the ceremony, Leland’s uncle says, “Just kidding, no car!” Leland cannot prevail in a breach of contract claim because the agreement lacks: ___ Offer ___ Acceptance ___ Consideration ___ Legality ___ Mutual assent

5. Which of the following does not result in the termination of an offer? ___ Revocation ___ Acceptance ___ Rejection ___ Death of the offeror ___ Destruction of the subject matter

Nonparametric Methods
In this assignment, we will use the following nonparametric methods:

• The Wilcoxon signed-rank test: The Wilcoxon signed-rank test is the nonparametric test analog of the paired t-test.
• The Wilcoxon rank-sum test or the Mann-Whitney U test: The Wilcoxon rank-sum test is an analog to the two-sample t-test for independent samples.

Part 1: Wilcoxon Signed-Rank Test

Let's take a hypothetical situation. The World Health Organization (WHO) wants to investigate whether building irrigation systems in an African region helped reduce the number of new cases of malaria and increased the public health level.

Data was collected for the following variables from ten different cities of Africa:

• The number of new cases of malaria before the irrigation systems were built
• The number of new cases of malaria after the irrigation systems were built

Table 1: Cases of Malaria

Using the Minitab statistical analysis program to enter the data and perform the analysis, complete the following:

• Run a sample Wilcoxon signed-rank test to show whether there is a statistically significant difference between the number of cases before and after the irrigation systems were built.
• Obtain the rank-sum.
• Determine the significance of the difference between the groups.
• Determine whether building these systems helped reduce new cases of malaria.
• In a Microsoft Word document, provide a written interpretation of your results.