1.Of 84 adults selected randomly from one town, 62 have health insurance. Find a 90% confidence interval for the true proportion of all adults in the town who have health insurance.
2. The duration of telephone calls directed by a local telephone company: σ=4.2 minutes, n=500, 97% confidence. Use the confidence level and sample data to find the margin of error E.
A. 0.018 min
B. 0.408 min
C. 0.009 min
D. 0.087 min
3. How many commuters must be randomly selected to estimate the mean driving time of Chicago commuters? We want 98% confidence that the sample mean is within 2 minutes of the population mean, and the population standard deviation is known to be 10 minutes.
4. Thirty randomly selected students took the calculus final. If the sample mean was 89 and the standard deviation was 6.2, construct a 99% confidence interval of the mean score of all students. Assume that the population has a normal distribution.
5. α=0.05 for a two-tailed test. Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis.
6. In a sample of 47 adults selected randomly from one town, it is found that 9 of them have been exposed to a particular strain of the flu. Find the P-value for a test of the claim that the proportion of all adults in the town that have been exposed to this strain of the flu is 8%.
7. For a simple random sample, the size is n=17, σ is not known, and the original population is normally distributed. Determine whether the give conditions justify testing a claim about a population mean µ.
8. A medical researcher claims that 20% of children suffer from a certain disorder. Indentify the type I error for the test.
A. Fail to reject the claim that the percentage of children who suffer from the disorder is equal to 20% when the percentage is actually 20%.
B. Reject the claim that the percentage of children who suffer from the disorder is different from 20% when that percentage really is different from 20%.
C. Fail to reject the claim that the percentage of children who suffer from the disorder is equal to 20% when that percentage is actually different from 20%.
D. Reject the claim that the percentage of children who suffer from the disorder is equal to 20% when that percentage is actually 20%.
9. It is commonly accepted that the mean temperature of human is 98.6oF. Yours truly XXXXX XXXXX better to do but measured the temperatures of 26 colleagues 1 to 4 times daily to get a total of 123 measurements. The collected data yielded a sample mean of 98.4oF and a sample standard deviation of 0.7oF. Is the mean temperature of his colleagues less than 98.6oF at the 0.01 significance level? Justify your answer with the proper statistics.
10. My brother wants to estimate the proportion of Canadians who own their house. What sample size should be obtained if he wants the estimate to be within 0.02 with 90% confidence if
a. He uses an estimate of 0.675 from the Canadian Census Bureau?
b. He does not use any prior estimates?
11.The recommended daily allowance (RDA) of cobalamine (Vitamin B12) for growing teens is 2.4 µg (micrograms). It is generally believed that growing teens are getting less than the RDA of 2.4 µg of cobalamine daily.
A not-to-be-named Pharmaceutical (ntbnP) peddles dietary supplements around the country. It is claimed by ntbnP representatives that by taking their vitamin supplement, teens will have the RDA of cobalamine. FDA is going to take on ntbnP to show that the supplement comes short of providing teens with the recommended RDA.
FDA managed to collect with a 24-hour period blood sample of 10 randomly selected teens around the country. The amounts of cobalamine (in µg) determined in these 10 randomly selected teens are given as follow:
1.85 2.35 1.87 1.90 1.37 2.35 2.55 2.28 1.95 2.49
Based on their national experience, FDA assumes that the the population standard deviation of cobalamine in teens to be 0.56 µg.
Now, you are asked to weigh in on the dispute between FDA and ntbnP.
a. Given the above information, what kind of hypothesis test will you conduct? z-test, t-test, χ2-test, F-test, or Ω-test? Please explain.
b. What will be the null hypothesis, the alternative hypothesis, and, hence, the “tailedness” of the test (left-tailed, right-tailed, or two-tailed)?
c. What is be the corresponding test statistics?
d. What is the corresponding p-value of the hypothesis test?
e. What kind of conclusion can you draw from the hypothesis test you have just performed? Of course, representatives of ntbnP would like to have the conclusion skewed to their advantage. And so would the officials from FDA. What would you do if you are representing ntbnP? But, if you are representing FDA, how would you present your argument?
f. But, wait. What if FDA actually does not know the population standard deviation in this case, would you conduct your hypothesis test different? Just in case that you are going to perform the hypothesis different, what would you do instead?
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