Scenario I

You are the manager of the Gander Mountain store in Frogtown, IL. Recently, a customer mentioned that they believed your prices for ammunition were lower than the prices of Gander Mountain’s primary competitor in the hunting equipment store Cabela’s. You would like to be able to include that statement in a forthcoming print advertisement, so you need statistical evidence to support the assertion. 1. Identify the null and alternative hypothesis needed to test the contention. We are concern about the ammunition ($) difference between Gander Mountain (u1) and Cabela’s (u2). Null: Ho: Gander Mountain (u1) < Cabela’s (u2)

Alt: Ha: Gander Mountain (u1) > Cabela’s (u2)

Based on information from outside consumer the null hypothesis that our brand (u1) prices are less than competitor brand (u2) is rejected, making the alternative hypothesis (u1) with higher prices to be accepted. 2. Then identify the most appropriate sample section technique to gather data for testing the hypothesis. Use a probability sample or simple random sample technique for both companies; generating random sample purchase dates and various ammunition purchases. 3. What statistical test should you use to accept or reject this hypothesis using the data you will collect? If the standard deviation is unknown, we assume the t-test will work since we have two independent samples. Option 2: t-test or z-test has equal value and both tests could be used if the independent sample size is large enough.

Scenario II

Your love of golf has brought you back to the range as the new product manager for UniDun’s Straight Flight (SF) line of golf balls. The company’s research and development group has been experimenting with dimple patterns that promote straight flight and feel they have achieved some degree of success. You, however, are worried about the effect that the new pattern might have on driving distance. The Golf Ball Distances document in the Updates and Handouts section contains test results that compare the driving distance for the two different kinds of balls: 40 balls of the new SF type, and 40 of the old UniDun type. Your job is to determine if the old UniDun balls can be driven further than the new SF balls. To resolve this question, you need appropriate answers to the following four questions.

Remember to use your Business Statistics in Practice textbook, the SI session archives, and the optional course resource to help you answer each question: 1. Identify the appropriate null and alternative hypothesis for this test. Express each in writing and in form of an equation. I have to determine our incumbent (brand) UniDun balls (u1) will still have greater distance (being driven) than new design SF balls (u2). Null: Ho: UniDun (u1) < SF (u2)Alt: Ha: UniDun (u1) > SF (u2) 2. Identify the appropriate statistical test to accept or reject the null hypothesis. The t-test should be used to test the null hypothesis, since both groups are independent samples and the standard deviation is unknown. One-tail test should be used for the alternative hypothesis. 3. Calculate the statistical parameters, the mean, variance, and standard deviation. Then calculate the statistical test and p-value.

Scenario III

As the food court manager at the Mall of Elbonia, you need to determine how much time customers spend at the mall during different times of the week (for example: midweek day; midweek evening; weekend day; weekend evening). Last week the mall survey staff randomly surveyed mall visitors as they left the mall. One key question asked how much time the customer had spent in the mall on that day. The findings from this study are provided in the document titled Mall Time Results, provided in Resources. Columns A through D show the time spent by the customers interviewed, according to the part of the week and time of day when the interviews occurred. Is there any statistically significant difference (at alpha = .05) in the average amount of time people spend in the mall based on the part of the week and time of day? To determine the answer to the question, you need appropriate answer to all of the following four questions.

Remember to use your Business Statistics in Practice textbook, the SI session archives, and the optional course resources to help you answer each question: 1. Identify the null and alternative hypothesis you should form for this test. Express each in writing and also in equation form. In this analogy, I must determine the amount of time each customer spends at the mall from days to weeks. Then figure out the means of the four variances and then determine what between and within these means.

The population average for Midweek Day, Midweek, Evening, Weekend Day, and Weekend Evening, were there is significant difference means (u1, u2, u3, and u4). We want the null hypothesis test Ho: u1 = u2 = u3 = u4 and alternative hypothesis Ha: u1,u2, .. or more will be different for the others. 2. Identify the appropriate statistical test to accept or reject the null hypothesis. In comparing of three means or more in the sample groups, we assume the statistical test would be the ANOVA – F test. Thus null hypothesis will be rejected based on the observation from F (statistic) greater than F (critical).

3. Calculate the appropriate statistical test values to accept or reject your null and alternative hypothesis.

Anova: Single Factor

SUMMARY

Groups

Count

Sum

Average

Variance

Midweek, Day

25

2087.899

83.51596

1300.167

Midweek, Evening

25

2384

95.36

1479.657

Weekend, Day

25

2528

101.12

2434.610

Weekend, Evening

25

3074

122.96

2608.457

ANOVA

Source of Variation

SS

df

MS

F

P-value

F crit

Between Groups

20487.12

3

6829.04

3.492

0.019

2.699

Within Groups

187749.4

96

1955.723

According to the data analysis, the observation indicates f statistic is 3.492, is greater than F critical statistic 2.699. In this situation we reject the null hypothesis based on alpha = .05.

4. What should you tell the Mall of Elbonia’s food court stores manager in terms of the mall’s high-traffic time and customer tendencies? Even though our ANOVA analysis recommends the null hypothesis to be rejected, the alternative is positive with amounts of customers spending time in the mall on daily and weekly basis. This allow us to re-group and create strategic plan by partnering with our fellow store merchants, when they have scheduled sales events and blockbuster season end sales; by promoting discounts or other incentives during those scheduled events. Based on data the foot traffic will continue to visit regardless of sales, the key point is word of mouth to generate profits.