The following data is based on a study by the American heart association on how age, blood pressure, and smoking can predict the risk of a stroke.
a. Write the multiple regression equation.
b. What are R2 , P-value-, and F here? What is significant? What is strong?
c. Based on your model, What is the risk level of a 50 years old smoker whose average Blood pressure is 135?
d. Explain its statistical significance.
e. Drop one less significant variable and try again- Rerun the model. Is it a better model? In what way? Explain.
risk 12 24 13 56 28 51 18 31 37 15
Age 57 67 58 86 59 76 56 78 80 78
Pressure 152 163 155 177 196 189 155 120 135 98
smoker N N N Y N Y Y N Y N
2. Suppose the historical average work week was 39.2 hours and SD was 4.8 hours as reported by the labor Dept. This year a study of 112 workers showed a mean of 38.5 hours. Test whether the workweek is the same or significantly shorter due to the recession. (Left tail). Use a .01 significance level.
a. Calculate the appropriate Z or T —————————–
b. What is the appropriate Critical value T or Z ——————————–
c. Statistical conclusion —————————————————-
d. Practical conclusion —————————————————————
3. A Shell oil company executive says (Claims) that a majority of workers – more than 50% – prefer a 10 hour four day work week over an 8 hour five day work week. Of a 105 worker sample, 67 said they prefer a 10-hour-4-day work-week. At alpha- significance level of .01 does this sample support the executive’s suggestion (more than 50%, right tail)
a. Critical Value
b. What is the appropriate calculated test statistic T or Z
c. Statistical conclusion
d. Practical conclusion
4. The financial industry Earnings average per share last year were $3. This year, earnings per share in 10 financial companies were as follows. Test the hypothesis that this year’s earnings do not differ from last year – at alpha (significance level) =.01
Data 1.92, 2.16, 3.63, 3.16, 4.10, 3.14, 2.20, 2.34, 3.10, 2.38
Hypothesis being tested : Mean=3
a. Critical Value T or Z
b. What is the appropriate
c. Statistical conclusion
d. Practical conclusion
5. A study showed that 110 of 200 people say that their major source of news is TV.
a. What would be a 99% confidence interval for the proportion? _________
b. What i s the minimum appropriate sample size if you want to re-conduct that survey
6. A sample of 100 CNN viewers shows an average household income of 119 K and a standard deviation of 30k.
a. What would the 99% confidence interval of the mean be? ___________
b. Comment on the width of the interval.
7. Confidence interval : On a scale of 1-100, a sample of 10 restaurant guests showed a mean customer satisfaction level of 71 points and a standard deviation of 5 points. At 99%, what would be the confidence interval of the mean?
8. Two Samples Z test: Male and female muscle flexibility were measured and reported as follows. Test the hypothesis of mean equality at.01 level of significance.
Sample mean SD
Male 45 18.64 3.29
Female 31 20.99 2.07
a. Hypothesis being tested: M1=M2
b. Critical Value
c. What is the appropriate calculated T or Z
d. Statistical conclusion
e. Practical conclusion
9. ANOVA: Children attention span in seconds to TV commercials was measured for clothes, food and toys commercials. The data is as follows.
clothes 26 21 43 35 28 31 17 31 20
food 45 48 43 53 47 42 34 43 57 47 44 54
toys 60 51 43 54 63 53 48 58 47 51 51
a. What do you conclude about the variation in these three types of commercials?
b. Conduct one more pairwise comparison at .01 significance . Compare a pair of means (M1=M2) use Z. (I know, it is not very accurate) What is the conclusion?
10. In the clinical trials of the allergy medicine Clarinex, 50 out of 1655 individuals reported having dry mouth. In the placebo control group, 31 out of 1652 reported having a dry mouth as a side effect. Test the equality of proportions VS the alternative hypothesis that Clarinex causes dry mouth – at .01 significance level.
c. Hypothesis being tested?
d. Critical Value
e. What is the appropriate Z
f. Statistical conclusion
g. Practical conclusion
11. Eight operating rooms were tested to see if a bacterial soap has reduced the contamination rates. The data shows the contamination in each room the year before and the year after using the soap. What do you conclude at .01 significance level
Before: 6.6 6.5 9 10.3 11.2 8.1 6.3 11.6
After: 6.8 2.4 7.4 8.5 8.1 6.1 3.4 2
h. Hypothesis being tested: equality of means. Should it be a one tail test?
i. Critical Value at .01?
j. What is the appropriate calculated T or Z
k. Statistical conclusion
l. Practical conclusion. Does the contamination level change?
1. Article Critique: In this article, the author examines the status of Jobs and gender in the US economy. Describe: the questions (Hypothesis) addressed, the statistical methods used (including significance and graphs) and the conclusions. Be critical. But you do not have to understand everything. Will “Care” work continue to bias the job growth towards women? The article: “The Care Economy: Gender, Economic Restructuring, and Job Polarization in the US. Labor Market. Author: Rachel Dwyer. Source: American Sociological Review. You can obtain the article through EBSCO database.
2. Summarize four of Nassim Taleb’s criticisms of our traditional statistical methods. Give examples.
3. Explain two practical ideas from “Black Swan” that may improve your decision making/job/business/industry/ or career planning?
4. Summarize four Greenspan’s explanations – reasons – for the financial crisis of 2008? Are statistical methods one to blame?