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Math 3339
Section 19377
MWF 10-11am SR 116
(and section 20582 – online)
Bekki George
[email protected]
639 PGH
Office Hours:
11:00 - 11:45am MWF or by appointment
Thursday online 5-7 pm
EMCF 26
1. A politician wants to know what percentage of the voters support her position
on the issue of forced busing for integration. What voter sample should be
obtained to determine with 90% confidence the support level to within 4%?
a. 21
b. 25
c. 423
d. 601
e. 1691
2. A study was carried out to investigate the effectiveness of a treatment. 1000
subjects participated in the study, with 500 being randomly assigned to the
“treatment group” and the other 500 to the “control (or placebo) group”. A
statistically significant difference was reported between the responses of the
two groups (p-value < .005). Thus,
a. there is a large difference between the effects of the treatment and the
placebo.
b. there is strong evidence that the treatment is very effective.
c. there is strong evidence that there is some difference in effect between the
treatment and the placebo.
d. there is little evidence that the treatment has any effect.
e. there is evidence of a strong treatment effect.
3. Suppose we have two SRSs from two distinct populations and the samples are
independent. We measure the same variable for both samples. Suppose both
populations of the values of these variables are normally distributed but the
means and standard deviations are unknown. For purposes of comparing the
two means, we use
a. Two-sample t procedures
b. Matched pairs t procedures
c. z procedures
d. none of these
Section 9.5 - Inferences Concerning Two Population Variances
The F – distribution:
X 1 / v1
F=
X 2 / v2
X 1 , X 2 are chi-squared rv's
v1 is the number of numerator degrees of freedom
v2 is the number of denominator degrees of freedom
Example:
Mixed Examples:
Do you have an insatiable craving for chocolate or some other food? Since many
North Americans apparently do, psychologists are designing scientific studies to
examine the phenomenon. According to the New York Times (Feb. 22, 1995), one
of the largest studies of food cravings involved a survey of 1000 McMaster
University (Canada) students. The survey revealed that 97% of the women in the
study acknowledged specific food cravings while only 67% of the men did.
Assume that 600 of the respondents were women and 400 were men. Is there
sufficient evidence to claim that the true proportion of women who acknowledge
having food cravings exceed the corresponding proportion for men?
The true average tread lives of two competing brands of radial tires (brand X and
brand Y) are known to be normally distributed. The standard deviation of brand X
tires is known to be 2200, and the standard deviation of brand Y tires is known to
be 1900. A sample of 45 brand X tires results in a sample mean of 42,500 and
sample standard deviation of 2450. A sample of 45 brand Y tires results in a
sample mean of 40,400 and sample standard deviation of 2150. Find a 95%
confidence interval for the difference in the true means, mean of X minus mean of
Y.
In an experiment to study the effects of illumination level on performance,
subjects were timed for completion in both a low light level and high light level.
The results are below.
Low
Light
High
Light
Subject
1
2
3
4
5
26
29
32
26
18
21
23
20
6
7
8
9
21 41
25
25
27
20 25
16
16
25
Can you say with 95% certainty that the average completion time is lower in high
light?
EMCF 26
4. For a fixed confidence level, when the sample size increases, the length of the confidence interval for a population mean decreases. a. True b. False 5. The z score corresponding to a 98 percent confidence level is 1.96. a. True b. False