# OU Inferential Statistics Tables

The table below shows the observed frequencies of different kinds of crime in threeneighborhoods.

Violence

Theft

Vandalism

Neighborhood1

16

25

42

Neighborhood2

15

18

16

Neighborhood3

39

36

30

Total

70

79

88

What is the expected frequency of violence in Neighborhood3? Round your answer to the

nearest whole number (i.e. no decimal places).

The table below shows beer, water and wine sales at three different sports games. Calculate the Chisquare value and report the value in full.

Observed Frequencies

Soccer

Tennis

Hocke

Beer

9

5

9

Water

6

9

5

Wine

7

11

8

Total

22

25

22

Hocke

To help you out, below we’ve provided a table with some of the expected frequencies:

Observed Frequencies

Soccer

Tennis

Beer

7.33

8.33

Water

6.38

Wine

8.29

Total

22

25

22

A baker is interested in whether there is an association between three types of cookies,

and gender of the buyer. He finds the following contingency table, and a significant Chisquare value of 10.584.

Men

Women

Chocolate

11

11

Nuts

22

9

Fruit

8

20

Calculate Cramer’s V for this table.

Yoncebé is selling tickets for her new tour. She wants to see the change in ticket sales, as a

result of price.

Based on data from previous tours, Yoncebé has found the regression equation: number

of tickets = 3000 – 7.3x, where x = ticket price.

If Yoncebé prices the tickets at $50, how many tickets is she predicted to sell?

You look at the relationship between how much time people spend on the website

‘Bookface’ and how productive they are at work. You assume that time spent on Bookface

is the predictor variable, and time spent working is the response variable. The correlation

between minutes spent on Bookface and minutes spent working is -0.5. The standard

deviation in Bookface time is 4.86, and the standard deviation of time spent working is

3.50.

You want to find the values for the equation ŷ_i = a + bx_iy^i=a+bxi. What is the value

of the slope?

Calculate the total sum of squares for the table below.

Predicted scariness

Observed scariness

2.88

3.8

3.22

2

3.56

4

3.90

3

4.24

5

Mean = 3.56

Mean = 3.56

Calculate the regression sum of squares for the table below

Predicted scariness

Observed scariness

2.88

3.8

3.22

2

3.56

4

3.9

3

4.24

5

Mean = 3.56

Mean = 3.56

Based on the regression sum of squares and total sum of squares you calculated in the previous two

questions. Calculate the R-squared.

Sometimes it’s scary to ask people out on dates, and sometimes it’s easier. A dating researcher decides

to try to build a model to predict how likely a person is to ask someone on a date based on the

following predictors: level of attraction, amount of loneliness, desperation, fear of rejection.

How many parameters are in the model?

After 20 observations, the model predicting how likely a person is to ask someone on a date based on

level of attraction, amount of loneliness, desperation and fear of rejection has an error sum of squares

of 10.6 and a total sum of squares of 26.2.

What is the F-test statistic?

Your null hypothesis was that the regression coefficients for level of attraction, amount of loneliness,

desperation and fear of rejection are all 0.

What is the threshold value above which the F-statistic must lie in order to reject the null hypothesis at

the 0.05 level? Use the F-table in the formulas and tables document and round the value to three

decimal places.

A TV company is interested in the people watching their period drama show “Downtown Castle” that is

set in the early 1900s. They found an overall F-statistic suggesting that together, age and hours of free

time significantly predicted the number of episodes of Downtown Castle that people watched in a

sample of 30. The slope coefficient for age was 4.5, with a standard error of 2.5

What is the t-value of the predictor age?

Based on the Downtown Castle model, calculate the upper boundary of the 95% confidence interval for

the age slope coefficient. You can select the critical t-value from the table.

Based on the Downtown Castle model, calculate the lower boundary of the 95% confidence interval for

the age slope coefficient.

The company decides to look at three other prizes in addition to cash and vouchers: a car,

a holiday and a computer.

How many dummy variables will the company use in their model?

Some of us need a little help to keep our energy levels up when we’re learning statistics. You run an

experiment where you give people energy drinks, and see how many statistics chapters they complete.

The table below shows the number of statistical tests people learned after drinking energy drinks. One

group drank a can of ‘Blue Cow’, one group drank a can of ‘Popstar’ and one drank a can of ‘Demon’.

Blue Cow

Popstar

Demon

3

3

2

5

6

4

4

5

5

7

8

6

Mean = 4.75

Mean = 5.5

Mean = 4

Calculate the within-group variance for your data.

The table below shows the number of statistical tests people learned after drinking energy drinks.

Blue Cow

Popstar

Demon

3

3

2

5

6

4

4

5

5

7

8

6

Mean = 4.75

Mean = 5.5

Mean = 4

Calculate the between-group variance for your data. The grand mean is 4.83

The table below shows mean tomato sales for each location. The within-group sum of

squares was 102.

Window

Cash desk

Outsid

15

25

10

Calculate the lower 95% confidence interval boundary for the difference between the cash

desk location, and outside location (in your calculation use: cash desk – outside). Use an

alpha level of 0.05.

You’re interested in Wayne East’s new album. People seem to be very excited about it, but

is it really that good? You ask your friends to rate it on a scale of 1 to 4, and expect that the

median score will be higher than 2. Your friends ratings were 3.5, 4.2, 2.3, 3.0 and 1.0.

You decide to check this with a Wilcoxon signed rank test. What is the test statistic?

You’re still not convinced of your findings about Wayne East’s album, so you decide to do

an experiment on how happy people are after listening to Wayne’s new album, and

compare this to a group that listen to a lecture on Astrophysics. The table below shows

the enjoyment levels in both groups.

Wayne

Astrophysics

2.5

8.0

7.4

5.5

7.2

3.2

6.5

6.2

What is the sum of the ranks in the Wayne group?

Based on the table in the previous question, what is the sum of the ranks in the

Astrophysics group?

Based on comparing the Wayne East and Astrophysics, what is the test statistic if we run a

Wilcoxon rank sum test?

From this question onwards, please round all values used in calculations to 5

decimal places.

The researcher was interested if the mean course duration is different for students from

specific faculties, namely Business and Economics, Law and Social Sciences. To

investigate this, they used a one-way ANOVA. The table below shows the descriptive

statistics.

Faculty

Mean

N

Business and Economics

81.11111

9

Law

45.44444

9

Social Sciences

63.88889

9

Total

63.48148

27

What is the F value associated with this ANOVA?

All the students begin their courses with an introductory course. The researcher wonders

if the proportion of students who passed the introductory course is equal to the

proportion who graduated. The table below shows the proportions.

Not graduated

Graduated

Not passed introductory

97

81

Passed introductory

64

158

Total

161

239

What is the p-value associated with the test statistic for two-sided test?

Course duration was predicted through a multiple regression test using procrastination,

IQ, gender, achievement motivation and failure anxiety. See sum of squares output below.

Sum of Squares

df

Mean Square

Regression

8275.689

5

1655.138

Residual

50173.825

140

358.384

Total

58449.514

145

What is the multiple correlation value?

Course duration was compared across three faculty groups. The table below shows the

mean rank for these groups (higher ranks mean longer course duration).

N

Mea

Business and Economics

12

26.0

Law

9

7.61

Social Sciences

15

19.0

Total

36

The mean rank is (36+1)/2 = 18.5. What is the value of the test statistic if a non-parametric

test is used?

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