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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