School

York UniversityDepartment

ManagementCourse Code

MGMT 1050Professor

William(bill) WoofStudy Guide

FinalThis

**preview**shows pages 1-3. to view the full**10 pages of the document.**Part I - Problem Recognition (24 marks, 3 marks each) – 2 for hypotheses, 1 for test

ALEX

1.

A ski company in Whistler owns two ski shops, one near

Whistler and one near Blackcomb. The following data were

collected from both stores:

Whistler

shop

Blackcomb

shop

Mean sales $328 $435

Sample std. Dev. $104 $151

Sample size 35 days 30 days

The company would like to test for a difference in daily

average goggle sales between the two stores

H0: µw − µB = 0

HA: µw − µB ≠ 0

Test: t test

Not equal variance

2.

The state lottery office claims that the average household

income of those people playing the lottery is greater than

$37,000. They also know that the distribution of these

households’ income is normal with a standard deviation of

$5,756. To test their claim a sample of 25 households was

studied. It was found that the average income in the sample

was $36,243.

H0: µ < 37,000

HA: µ > 37,000

Test: Z test

3.

In random samples of 1000 people in the United States and

in France, 70% of the people in the Unites States and 75%

of the people in France indicated that they were positive

about the future economy. Does this provide strong

evidence that the people in France are more optimistic

about the economy?

H0: pF − pUS < 0

HA: pF − pUS > 0

Test: Z test

4.

The distributor of the post, a regional newspaper serving

North York is considering three types of dispensing racks.

Management wants to know if the different racks affect

sales. These racks are designated as J-1000, D, and UV-57.

Management also wants to know if the placement of the

racks either inside or outside supermarkets affects sales.

Each of six similar stores was randomly assigned a machine

and location combination, and data were collected on the

number of papers sold over four days.

Ho: no interaction

Ha: interaction

Ho: µj-1000 = µD = µUV57

Ha: at least two means differ

Ho: µinside = µoutside

Ha: at least two means differ

Two-way ANOVA

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ERINDA

5.

A pasta chef was experiencing difficulty in getting brands of

pasta to be cooked just right. The main problem she

experiences is with the speed of water absorption by the

different pasta brands. Pasta with a faster rate of water

absorption has a greater tendency to be overcooked. She

decides to conduct an experiment in which two brands of

pasta, one Canadian and one Italian, were cooked for either

4 or 8 minutes. The variable measured was the speed of

water absorption in each case. The results were then

recorded an analyzed.

Ho: no interaction

Ha: interaction

Ho: µc = µI

Ha: at least two means differ

Ho: µ4 = µ8

Ha: at least two means differ

Two-way ANOVA

6.

A large milling machine produces steel rods to certain

specifications. The machine is considered to be running

normally if the standard deviation of the diameter of the rods

is 0.15 millimeters. As line supervisor, you need to test to

see whether the machine is operating normally. You take a

sample of 25 rods and find that the sample standard

deviation is 0.19.

H0: σ2 = 0.0225

HA: σ2 ≠ 0.0225

Test: χ2

7.

Are medical students more motivated than law students? A

randomly selected group of each were administered a

survey of attitudes toward life, which measures motivation

for upward mobility. The scores are summarized below

(higher scores mean greater motivation).

Medical Students Law Students

Sample Size 250 100

Mean Score 83.5 80.2

Pop. Std. Dev. 11.2 9.2

H0: µM − µL < 0

HA: µM − µL > 0

Test: z test

8.

In a recent survey, college students were asked the amount

of time (in hours) they spend weekly watching television and

surfing on the Internet. The researchers were interested in

determining whether the time spent on both activities was

equal. They collected the following data:

Person # 12345678

Internet 2 7 3 8 9 15 7 2

TV 4 15 5 3 4 4 4 8

H0: µd = 0

HA: µd ≠ 0

Test: t test

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Part II – True/False (15 marks, 1 mark each) VANESSA

True False

1. In a simple regression model, if the regression model is deemed to be statistically

significant, it means that the regression slope coefficient is significantly greater than

zero

X

2. In a hypothesis test, the p-value measures the probability that the alternative

hypothesis is true.

X

3. If a hypothesis test is conducted for a population mean where only non-negative

values can be sampled, a null and alternative hypothesis of the form: H0 : μ = 100, Ha : μ

≠

100, will result in a one-tailed hypothesis test since the statistic can only assume non-

negative values

X

4. Two variables have a correlation coefficient that is very close to zero. This means

that there is no relationship between the two variables.

X

5. All other things held constant, increasing the level of confidence for a confidence

interval estimate for the difference between two population means will result in a wider

confidence interval estimate.

X

6. The method used in regression analysis for incorporating a categorical variable (no.

of categories = 5) into the model is by organizing the categorical variable into five

dummy variables.

X

7. In a recent one-way ANOVA test, Mean SSW was equal to 1,590 and the Mean SSB

was equal to 310. Therefore, SST is equal to 1,900.

X

8. A local medical center has advertised that the mean wait for services will be less

than 15 minutes (but more than 0 minutes). Given this claim, the hypothesis test for the

population mean should be a one-tailed test with the rejection region in the lower (left-

hand) tail of the sampling distribution.

X

9. Consider the following regression equation: ŷ = 356 + 18.0x1 – 2.5x2. The x1 variable

is a quantitative variable and the x2 variable is a dummy with values 1 and 0. Given this,

we can interpret the slope coefficient on variable x2 as follows: holding x1 constant, if the

value of x2 is changed from 1 to 0, the average value of y will increase by 2.5 units.

X

10. The coefficient of determination measures the percentage of variation in the

independent variable that is explained by the dependent variables in the model.

X

11. A perfect correlation between two variables will always produce a correlation

coefficient of +1.0.

X

12. The prediction interval developed from a simple linear regression model will be at its

narrowest point when the value of x used to predict y is equal to the mean value of x.

X

13. When testing a hypothesis about the variability of a population, the statistical

requirements call for us to convert the variance to standard deviation and run a chi-

square test

X

14. When the expected cell frequencies are smaller than 30, the cells should be

combined in a meaningful way such that the expected cell frequencies do exceed 30.

X

15. If it is known that a simple linear regression model explains 56 percent of the

variation in the dependent variable and that the slope on the regression equation is

negative, then we also know that the correlation between x and y is approximately (-

0.75)

X

16. In estimating the difference between two population means, if a 95 percent

confidence interval includes zero, than we can conclude that there is a 95 percent

chance that the difference between the two population means is zero.

X

17. In a multiple regression analysis, even if only some of the independent variables

have values equal to zero, the regression intercept, b0, can still be meaningful.

X

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