Download (02): Introduction to Statistical Methods

University of Saskatchewan
College of Arts & Science
Department of Mathematics and Statistics
STATS 245.3 (02): Introduction to Statistical Methods
Instructor: M. Szafron
Assignment #3
Due:
1. For a random sample of 20 Brand X cigarettes, it was found that the mean nicotine content was 4.18
milligrams and the standard deviation was 0.3 milligrams. Assuming normality, construct a 99% confidence
interval for the true mean nicotine content of Brand X cigarettes.
2. Take a thumbtack and drop it on a flat table. It either lands with its point up or else it lands on its side with its
point touching the table. Do this 50 times. A group of Grade 6 students claimed that half of the time the
thumbtack lies with its point up. Determine, at the 95% confidence level, whether your experiment supports
their claim. Remember to also calculate the corresponding p-value.
3. In a random sample of 47 Canadian men, the mean height was found to be 172.5 cm and the standard
deviation was determined to be 6.25 cm. Test the hypothesis that the mean height of Canadian men is 175
cm against the alternative that it is not 175 cm. Work at a significance level of 0.01. Remember to also
calculate the corresponding p-value.
4. A manufacturer of widgets controls 40% of the market. The firm decides to put on a major advertising
campaign to increase sales. After two months they survey 500 potential customers and find that 220 bought
their product.
a. Can they conclude, at the 95% confidence level, that the advertising campaign was successful?
Remember to also calculate the corresponding p-value.
b. Calculate a point estimate for the true proportion of customers who bought widgets after the
campaign and state a 95% error margin, assuming the sample proportion is very close to the
population proportion.
c.
If the firm requires a 95% error margin of 0.01, how many customers need to be surveyed?
5. An opinion survey on the separation of Western Canada was administered to 120 people in SK and 150
people in BC. In both cases, the people were randomly selected. 25 of the respondents in SK and 40 of the
respondents in BC favored Western Canada’s separation.
a. At the 95% confidence level, does this indicate that British Columbians are more in favor of Western
Canada’s separation than people in SK?
b. Calculate a 95% confidence interval for the difference in the population proportions.
6. A medical doctor claims that his new technique for administering pain medication will decrease a patient’s
response time to the medication. A random sample of five patients who were administered pain medication
not using the doctor’s new technique claimed to feel no pain in times of 1.33, 1.43, 1.52, 1.32, and 1.33
minutes. Another random sample of five patients who were administered pain medication using the doctor’s
technique claimed to feel no pain in times of 1.05, 1.22, 1.49, 1.40, and 1.13 minutes. Assume normality.
a. Calculate the p-value associated with this problem and test the doctor’s claim at the 90%
significance level. Assume the variances between the two populations are equal.
b. Calculate a 90% confidence interval for the difference in the population means.
c.
Find a point estimate for the population mean response time for those patients who were
administered pain medication WITHOUT the doctor’s new technique and state a 90% error margin.
Remember to take into account this is a small sample!
STATS 245.3 (02): Introduction to Statistical Methods
7. An experiment was conducted on a sample of the U of S students, whose heights (in inches) before treatment
are listed below. The group of 32 students was subjected to an experimental growth hormone Laxon, a
derivative of processed primate pituitary glands. After one month, their heights (in inches) were measured
again, and are presented below.
Before Treatment
Student Heights In Inches
After Treatment
Before Treatment
After Treatment
59
58
64
64
65
65
67
67
68
69
69
69
71
71
73
73
62
62
64
65
66
66
67
69
68
68
70
72
72
74
74
76
66
67
67
67
68
68
70
70
72
72
76
75
63
65
65
66
66
66
67
67
69
69
71
71
72
73
77
78
a. Test, at the 90% significance level, whether, on average, the students were taller after the treatment.
b. Compute a 90% confidence interval for the mean change in student height.
c. Find a point estimate for the before-treatment, student-height population mean and a 90% error margin.
8. The following table provides the weight (lbs) and body length (cm) of female wolves. Assume that weight
depends on body length.
Weight (lbs)
Body Length (cm)
a.
b.
c.
d.
e.
f.
57
123
84
129
80
143
71
125
77
122
68
125
73
122
What percentage of the variability in the weight variable is explained by the linear relationship?
Calculate the line of best fit.
Calculate a 95% C.I. for the y-coordinate of the y-intercept and a 95% C.I. for the regression coefficient.
Calculate the residual sum of squares and estimate σ2.
At the 95% confidence level, can you conclude that your line of best fit goes through the origin (0,0)?
Justify your response.
At the 90% confidence level, can you conclude that your line of best fit suggest that an increase in a
female wolf’s body length will increase her body weight? Justify your response.
9. Let X be a random representing the heights of fathers and Y be a random variable representing the height of
the father’s son. The heights of 10 fathers and their sons are given in the following table.
Father’s Height 164.2 181.7 165
Son’s Height
176.3 175.6 174.4 179.5 181.5 175.3 177.3
170.7 177.5 174.3 178.8 167
174.4 168.6 183.9 183.7 168.6
y  0.265 x  128.399 ,
If the regression line is given by
a. What would be the expected of height of a son given his father’s height was 179 cm?
b. Calculate the 90% C.I. for the average height of sons who have fathers whose height is 172 cm.
c. If Bill’s father’s height is 173 cm, find the 95% prediction interval for Bill’s height.
d. For those sons whose height you would expect to be 176 cm, what average height would you expect their
fathers to have?
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