1. Suppose we are interested in examining the social basis of support for capital punishment. Could there be a relationship between religion (the independent variable) and support for capital punishment (dependent variable)? Suppose we administer a scale that measures support for capital punishment to a randomly selected sample that includes 20 individuals based on religious affiliation: Protestants, Catholics, Jews, people with no religious affiliation (“None”), and people from other religions (“Other”). Use the appropriate test and steps to calculate whether there is a relationship. Do this manually. (20 POINTS)

Calculating the probability that in a class of 20 students, there are at least two with the same birthday.

(a) First, calculate the probability that each student has a different birthday as follows (round to four decimal places)

b) Explain briefly why the above probability is calculated that way.

(c) Now note that the probability that there are at least two with the same birthday is the complement of the above probability. What is the probability that there are at least two with the same birthday

3. In the workbook on page 14, we solved the following problem:
A new type of light bulb has been developed which is believed to last longer than
ordinary light bulbs. To determine the average life of the new light bulb, a random sample of
100 light bulbs was tested. The sample had a mean life of 1960 hours. Estimate the true mean
life of the new light bulb using a 97% confidence interval. State your final conclusion using a
clear, complete sentence. Assume the population standard deviation is 142 hours.
For the confidence interval we calculated in this workbook problem, the confidence level
is 97%.
Using ZInterval on the calculator we found the 97% confidence interval for the mean life
was 1929.2 to 1990.8 hours. Based on this sample, we are 97% confident that the mean life
expectancy of all the new lightbulbs is between 1929.2 and 1990.8 hours.
The length of a confidence interval is (upper bound- lower bound). For this
confidence interval, the length is (1990.8-1929.2) = 61.6 hours.
To find the Margin of Error, using the length of a confidence interval, we use
EE = mmmmmmmmmmmm oooo eeeeeeeeee = llllnnnnnnnn oooo CCCC

22 . For this CI, EE = 61.6

2 = 30.8 hoooooooo.
To find the center of the CI, CCCCCCCCCCCC = (uuuuuuuuuu bbbbbbbbbb+llllllllll bbbbbbbbbb)

2

. The center of this CI is

CCCCCCCCCCCC = uuuuuuuuuu bbbbbbbbbb+llllllllll bbbbbbbbbb

2 = 1990.8+1929.2
2 = 3920

2 = 1960 hoooooooo, which is the sample
mean. Remember every confidence interval for the population mean is centered at the sample
mean.
(a) Now calculate confidence intervals for the mean expectancy of all the new lightbulbs using
confidence levels of 90%, 92%, 94%, 98%, and 99%. Determine the length, the margin of error
and center for each CI. I have filled in the information for the 97% confidence interval we
formed in the workbook.

Confidence level    Confidence Interval Length of CI Margin of Error Center of CI

90%
92%
94%
97% 1929.2 to 1990.8 hours   61.6 hours    30.8 hours 1960 hours
98%
99%

(b) As the confidence level increases, what happens to the width of the confidence interval? Use
clear, complete sentences to state and justify your answer.

(c) As the confidence level increases, what happens to the margin of error? Use clear, complete
sentences to state and justify your answer.

(d) As the confidence level increases, what happens to the center of the confidence interval? Use
clear, complete sentences to state and justify your answer.

A bridal shop is slow with deliveries. If Karen orders her dress 6 months before her rehearsal dinner, there is a 75% chance that the dress will arrive on time for her rehearsal dinner. If Karen forgets to order her dress 6 months early, there is only a 20% chance that the dress will arrive on time for her rehearsal dinner. Because Karen is so busy planning her wedding, she estimates that there is only a 90% chance that she remembers to order her dress 6 months early.

a) What is the probability that the dress arrives on time for Karen's rehearsal dinner?

b) If the dress arrives on time, what is the probability that Karen forgot to order her dress 6 months early?

Problem 6

The unemployment rate (UR) for PEI by quarter was as follows:

                                    UR           T (Time)

Year    Quarter            Rate     For Regression

2018    Q1                   12.0                 1

            Q2                   7.1                   2

            Q3                   8.2                   3

            Q4                   10.2                 4

2019    Q1                   12.2                 5

            Q2                   6.9                   6

            Q3                   7.1                   7

            Q4                   9.9                   8

1. Sketch this data on a graph. Is there seasonality in the data?
2. Use a four quarter moving average to determine the seasonal factors for the four quarters.

1. Calculate the four quarter moving average;
2. Centre the data if necessary;
3. Calculate the seasonal factors for each Quarter.
4. Calculate the average seasonal factors for each quarter.
5. What percentage is the rounding error in this calculation?

The following is a summary of data for 960 branch managers in the two major regions of a Canadian Bank:

1.   State the null and alternative hypotheses for a Chi Square test to determine if managers’ education level is dependent of which region they are from. (2 Points)

2.   State the rejection rule using the critical value approach. Let alpha = 0.05. (2 Points)  

3.   Calculate the expected frequency for the cell “No Degree” and “International Region” (2 Points)

4.   If the Chi Square statistic is 2.176, what is your conclusion? (2 Points)

Wall Street traders are anxiously waiting for the federal government’s release of the August numbers for nonfarm payrolls. Last year month of August showed an average of 120,000 new jobs with a standard deviation of 20,000. A sample of 100 nonfarm payrolls taken earlier in the week shows a sample mean of 117,000. Financial analysts often call such a sample mean the “whisper number”. Conduct a hypothesis test to determine whether the whisper number justifies a conclusion of a statistically significant change in the number of new jobs with respect to last year. Allow for 5% error in the test. The hypothesis setting for the test follows. H0 : µ = 120,000 Ha : µ ≠ 120,000 a. (5pt) Conduct hypothesis test using a critical-value approach. b. (3pt) Conduct a hypothesis test using a p-value approach. c. (3pt) According to the statistical analysis you have performed above, do you think the whisper number does justify a conclusion of a statistically significant change in the number of new jobs? WHY?

Clearwater National Bank wants to compare the account checking practices by the customers at two of its branch banks – Cherry Grove Branch and Beechmont Branch. A random sample of 28 and 22 checking accounts is selected from these branches respectively. The sample statistics are shown on the next slide

Cherry Grove                                  Beechmont

n                                        28                                            22

x                                        $1025                                       $910

s                                         $150                                         $125

Let us develop a 99% confidence interval estimate of the difference between the population mean checking account balances at the two branch banks.

Please, show work.

A manufacturer wants to compare the number of defects on the day shift with the number on the evening shift. A sample of production from recent shifts showed the following defects: Day Shift 5 8 7 6 9 7

Evening Shift 8 10 7 11 9 12 14 9

The objective is to determine whether the mean number of defects on the night shift is greater than the mean number on the day shift at the 95% confidence level.

State the null and alternate hypotheses.

What is the level of significance? What is the test statistic? What is the decision rule? Use the Excel Data Analysis pack to analyze the problem. Include the output with your answer. (Note: You may calculate by hand if you prefer). What is your conclusion? Explain. Does the decision change at the 99% confidence level?

Problem 5

Research into the relationship between hours of study and grades shows widely different conclusions. A recent survey of graduates who wrote the Graduate Management Admissions Test (GMAT) had the following results.         

Hours

Studied            Average

(Midpoint)      Score

40                    200

50                    290

65                    335

75                    445

85                    530

105                  650

95                    690

1. Run the regression analysis in Excel on this data. Include your output with your answer. (Note: You may calculate by hand if you prefer).
2. What is the regression equation for this relationship?
3. Use the regression equation to predict the average score for each category of hours studied.
4. Plot the original data and the regression line on a scatter gram. (You may use Excel).
5. How accurate is this regression at predicting GMAT scores based on hours studied? Explain.
6. Use the t statistic to determine whether the Correlation Coefficient is “significant” at the 95% confidence level.

2. An environmentalist is interested in estimating the mean time between eruptions of Old
Faithful Geyser in Yellowstone National Park. Over the course of a year, she takes a random
sample of the time intervals (in minutes) between eruptions. Her results are recorded in the
following table. Both the population mean and standard deviation are unknown.

Time Between Eruptions (in minutes)
63 63 71 77 81 65
67 84 72 75 70 70
93 83 85 79 90 74
81 74 80 65 70 84
83 78 71 67 97 88
62 61 57 86 70 77
78 75 67 89 93 81
86 65 70 77 83 76
76 67 99 75 76 83
97 93 73 81 85 90
(a) Construct a stem-and-leaf diagrams of the times using two lines per stem.
(b) Describe the stem-and-leaf diagram. When describing a graph, you must describe the shape,
center and spread.
(c) Form a 95% confidence interval for the mean time between all eruptions of Old Faithful
Geyser. Use clear, complete sentences to interpret the interval.
Confidence Interval
(d) Based on the 95% confidence interval formed in part (c), is it plausible that the mean time
between all eruptions of Old Faithfull geyser is 77 minutes? Why or why not? Use clear,
complete sentences to state and justify your answer.
(e) Based on the 95% confidence interval formed in part (c), is it plausible that the mean time
between all eruptions of Old Faithfull geyser is 90 minutes? Why or why not? Use clear,
complete sentences to state and justify your answer.

USE R software

Suppose that we want to test H₀ : F = G, where F is the distribution of weight for the casein feed group and G is the distribution of weight for the sunflower feed group of the chickwts data. A test can be based on the two-sample Kolmogorov-Smirnov statistic

chickwts
weight feed
1 179 horsebean
2 160 horsebean
3 136 horsebean
4 227 horsebean
5 217 horsebean
6 168 horsebean
7 108 horsebean
8 124 horsebean
9 143 horsebean
10 140 horsebean
11 309 linseed
12 229 linseed
13 181 linseed
14 141 linseed
15 260 linseed
16 203 linseed
17 148 linseed
18 169 linseed
19 213 linseed
20 257 linseed
21 244 linseed
22 271 linseed
23 243 soybean
24 230 soybean
25 248 soybean
26 327 soybean
27 329 soybean
28 250 soybean
29 193 soybean
30 271 soybean
31 316 soybean
32 267 soybean
33 199 soybean
34 171 soybean
35 158 soybean
36 248 soybean
37 423 sunflower
38 340 sunflower
39 392 sunflower
40 339 sunflower
41 341 sunflower
42 226 sunflower
43 320 sunflower
44 295 sunflower
45 334 sunflower
46 322 sunflower
47 297 sunflower
48 318 sunflower
49 325 meatmeal
50 257 meatmeal
51 303 meatmeal
52 315 meatmeal
53 380 meatmeal
54 153 meatmeal
55 263 meatmeal
56 242 meatmeal
57 206 meatmeal
58 344 meatmeal
59 258 meatmeal
60 368 casein
61 390 casein
62 379 casein
63 260 casein
64 404 casein
65 318 casein
66 352 casein
67 359 casein
68 216 casein
69 222 casein
70 283 casein
71 332 casein

1. Restate the question that the researcher is investigating?

2. What type of test is appropriate for this question?

3. Write out the model statements in words (make sure you include null model too)

4. What are the hypotheses (all of them)

5. Run the appropriate statistical test in Minitab (for this example you do not need to check for normality, variance, outliers etc, just run the test). Paste the output here. Paste it so it is easy to read.

6. Run a post-hoc test if appropriate. Paste results here as appropriate.

7. Summarize what the results are telling you. What is the take home message that you want to tell your audience. (I am not requiring a final graph for this assignment)

Salary course   Subject
1700 Humanities
1900   Humanities
1800 Humanities
2100 Humanities
2500   Humanities
2700   Humanities
2900   Humanities
2500   Humanities
2600   Humanities
2800   Humanities
2700   Humanities
2900   Humanities
2500   Social Sciences
2300   Social Sciences
2600   Social Sciences
2400   Social Sciences
2700   Social Sciences
2400   Social Sciences
2600   Social Sciences
2400   Social Sciences
2500   Social Sciences
3500   Social Sciences
3300   Social Sciences
3600   Social Sciences
3400   Social Sciences
2700   Engineering
2800   Engineering
2900   Engineering
3000   Engineering
2800   Engineering
2700   Engineering
3700   Engineering
3600   Engineering
3700   Engineering
3800   Engineering
3900   Engineering
2500   Managament
2600   Managament
2300   Managament
2800   Managament
3300   Managament
3400   Managament
3300   Managament
3500   Managament
3600   Managament