1. Multiple choice
1) Medical care and compensation costs for workers injured on the job vary and are strongly skewed. The National Academy of Social Insurance reports that the mean workers' compensation claim cost in a year is $439 per injured worker with a standard deviation of $20,000. The Central Limit Theoremstates:
A) an insurance company can get an average workers' compensation cost lower than the mean by insuring a large number of people
B) as a company insures more and more workers chosen at random, the average costs gets closer to $439
C) if a company insures a large number of workers chosen at random, that company's average claim cost will have approximately a Normal distribution
2) In which of these cases would the power become larger?
A) if the significant level is larger.
B) if the sample standard deviation is larger.
C) if the difference between population means is smaller.
D) all of the above
E) none of the above
3) Dyspnea, or shortness of breath, is a common complaint in patients with chronic obstructive pulmonary disease (COPD).
It is often assessed by an FEV1 test, measuring the forced expiratory volume in the first second.
A study examined the effects of various treatments on perceived dyspnea in patients with advanced COPD.
The researchers reported that for the 23 patients who had received 6 weeks of therapy with a long-acting bronchodilator, "there was a small, statistically insignificant, increase in FEV1.
What does "statistically insignificant" mean?
A). It means that you will not see increase in FEV1 from other samples.
B). It means that the differences observed were no more than you might have been expected to occur by chance even if the treatments had no effect on FEV1 results.
C). It means that the observed difference in FEV1 in the sample from the baseline FEV1 is not important.
D). It means that the results should not be trusted because the sample size is not enough.
4) Which of these settings does NOT allow use of a matched pairst procedure?
A. You interview both the husband and the wife in 64 married couples and ask each person about their ideal number of children.
B. You interview a sample of 64 unmarried male students and another sample of 64 unmarried female students and ask each about their ideal number of children.
C. You interview 64 female students in their freshman year and again in their senior year and ask each about their ideal number of children.
D. You interview 64 female students and their mothers and ask each about their ideal number of children.
5) A shipment of 1000 small lab mice arrives at the animal care facility with a Normal weight of 10 g per mouse. From this population of 1000 mice, a sample of 20 mice is selected and weighed. The average weight of the sample is 10.2 g. Suppose that the standard deviation of weight among mice in the 1000 mice (population) is 2 g, and 2.5 g for the 20 mice (sample).
If you retrieve (with replacement) many samples, each with a size 20, and get many means, then 95% of these means will be between (a____) +/- (b___)x(c___)
2. Fill in the blanks
1)
Different varieties of the tropical flower Heliconiaare fertilized by different species of hummingbirds. Over time, the lengths of the flowers and the forms of the hummingbirds' beaks have evolved to match each other. The following is an partial analysis of the length (mm) of the two color varieties. The researcher wants to know whether the length of yellow is significantly shorter than red variety.
Find the test statistics______________________, and p-value _____________
2) Arsenic is a compound naturally occurring in very low concentrations. Arsenic blood concentrations in healthy individuals are normally distributed with a mean of 3 mg/dl and standard deviation of 1 mg/dl.
Determine the required sample size to be able to use a 99% confidence interval to estimate the population mean within +/- 0.3 mg/dl ________________
3) The World Health Organization estimates that 5% of all adults in sub-Saharan Africa are living with HIV/AIDS. A survey takes a random sample of 1600 adults from all over sub-Saharan Africa and finds that 84 have HIV/AIDS.
Consider the all samples you can find (n=1600) from all over sub-saharan Africa, estimate the mean ________________and standard deviation_______________ of the sampling distribution of the sample proportions.
Find the probability that a random sample of 1600 adults in sub-Saharan Africa would have less than 4.5% living with HIV/AIDS __________________
3. The national average birth weight is 118 oz: N(mnatl =118, s = 24 oz). An SRS of 100 poor mothers gave an average birth weightof 115 oz. Is this statistically lower than the national average, at significance level 0.05?
Hypotheses: H0: mpoor = 118 oz (no difference with mnatl )
Ha: mpoor< 118 oz
a) Find the reject region of the hypothesis test
b) Find the power of the test if mpoor=110
c) In general, if mpooris actually 110, what is the probability of not rejecting the Ho?
d) In general, if mpoor is actually 118, what is the probability of rejecting the Ho?
4. Researchers are interested in whether the effects of DDT poisoning in rats are less extreme in males. An SRS of 100 male rats and an independent SRS of 100 female rats are obtained. The male rats had a sample mean of 39 and a sample standard deviation of 8. The female rats had a sample mean and standard deviation of 40 and 10, respectively.
a. Define the hypothesis.
b. Find the standard error of the difference in the means.
c. Find the test statistic
d. Find the p-value
5. Will customers rate their preferred drink higher than 6. (For example, if you prefer Pepsi, and you rate B is Pepsi, will the rating be greater than 6?)
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n
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Preference
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Before the experiment, I prefer pepsi over coke by (from -10 to 10)
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A is judged as
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A is rated as
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B is rated as
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1
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pepsi
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2
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coke
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2
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4
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|
|
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2
|
coke
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-4
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pepsi
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9
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6
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|
|
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3
|
coke
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-3
|
coke
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7
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3
|
|
|
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4
|
coke
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-10
|
coke
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10
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0
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|
|
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5
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pepsi
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9
|
coke
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5
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8
|
|
|
|
6
|
coke
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-4
|
coke
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7
|
4
|
|
|
|
7
|
pepsi
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9
|
coke
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2
|
9
|
|
|
|
8
|
coke
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-8
|
pepsi
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2
|
9
|
|
|
|
9
|
coke
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-4
|
coke
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7
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3
|
|
|
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10
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coke
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-4
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coke
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4
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4
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|
|
|
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mean = -1.7
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mean=5.5
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mean=5
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std=6.447
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std=2.953
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std=2.944
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a) Define clearly the hypothesis
b) Find the test statistic
c) Find the p-value
d) List all assumptions for the method you used in the question.