If I were taking this exam, and wanted to do well on it, I would:
Confidence Intervals Variable N Mean StDev SE Mean 95.0 % CI head 63 56.468 2.298 0.290 ( 55.889, 57.047) |
(i) H_{0}: µ = 54
(ii) H_{0}: µ = 56
(iii) H_{0}: µ = 58
(A) None | (B) Only (i) | (C) Only (ii) | (D) Only (iii) |
(E) (i) and (ii) | (F) (i) and (iii) | (G) (ii) and (iii) | (H) All |
(i) Everything else remaining the same, a 95% confidence interval based on 100 students would be shorter than the 95% interval given above.
(ii) Everything else remaining the same, a 99% confidence interval would be shorter than the 95% interval given above.
(iii) Everything else remaining the same, if the head circumferences of the sampled students varied more, a 95% confidence interval would be longer than the 95% interval given above.
(A) None | (B) Only (i) | (C) Only (ii) | (D) Only (iii) |
(E) (i) and (ii) | (F) (i) and (iii) | (G) (ii) and (iii) | (H) All |
(i) The p-value is the probability that the null hypothesis is true.
(ii) The p-value is the probability that we would observe a sample as extreme as we did under the assumption that the null hypothesis is true.
(iii) The p-value is the probability that the alternative hypothesis is true.
(A) None | (B) Only (i) | (C) Only (ii) | (D) Only (iii) |
(E) (i) and (ii) | (F) (i) and (iii) | (G) (ii) and (iii) | (H) All |
4. The number of years a person lives after being diagnosed with a certain disease is normally distributed with a mean of 4 years and a standard deviation of 1 year. Suppose a random sample of 16 people are selected from this diseased population. What is the probability that the sample will live an average of less than 3.5 years?
Questions 5 to 10 pertain to the following situation. The average serum cholesterol level in a certain group of patients is 240 milligrams. A new medication is designed to lower the cholesterol level in this population after one month. A sample of 60 people in the population used the medication for 30 days, after which their average cholesterol level was 232 milligrams with a standard deviation of 18 milligrams. The manufacturer of the new medication would like to see if the average cholesterol level in the population has been reduced.
5. Using statistical notation, specify the appropriate null and alternative hypotheses.
6. Calculate the p-value for the hypothesis test.
7. (4 pts.). Make a decision, "reject" or "do not reject," at the a = 0.05 level. Explain your reasoning.
8. (2 pts.) Based on the decision you made in question #7, what type of error might you have made?
9. (4 pts.) Calculate a 95% confidence interval for µ, the
average serum cholesterol level in the population after one month.
10. (2 pts.) Is your confidence interval in question #9 consistent with your decision in question #7? Explain.
(A) an observational study | (B) an experiment |
Question 12 pertains to the following situation. Can we
conclude that, on average, lymphocytes and tumor cells differ in size?
The following Minitab output tests the appropriate hypothesis using data
on the cell diameters of 40 lymphocytes and 50 tumor cells.
Two Sample T-Test and Confidence Interval Two sample T for Lympho vs Tumor N Mean StDev SE Mean Lympho 40 6.95 1.60 0.25 Tumor 50 17.92 2.97 0.42 95% CI for mu Lympho - mu Tumor: T-Test mu Lympho = mu Tumor (vs not =): T= -21.05 P=0.0000 DF= 88 Both use Pooled StDev = 2.46 |
__C__ 12. Which, if any, of the following could possibly describe the confidence interval for µLympho- µTumor that is missing from the output?
(i) ( -6.95, 17.92)
(ii) ( -12.01, -9.33)
(iii) ( -10.97, 10.97)
(A) None | (B) Only (i) | (C) Only (ii) | (D) Only (iii) |
(E) (i) and (ii) | (F) (i) and (iii) | (G) (ii) and (iii) | (H) All |
Two Sample T-Test and Confidence Interval Two sample T for FullTerm vs Premature N Mean StDev SE Mean FullTerm 12 10.38 1.40 0.40 Prematur 12 12.21 1.45 0.42 95% CI for mu FullTerm - mu Prematur: ( -3.04, -0.63) T-Test mu FullTerm = mu Prematur (vs not =): T= -3.16 P=0.0046 DF=22 Both use Pooled StDev = 1.42 Two Sample T-Test and Confidence Interval Two sample T for FullTerm vs Premature N Mean StDev SE Mean FullTerm 12 10.38 1.40 0.40 Prematur 12 12.21 1.45 0.42 95% CI for mu FullTerm - mu Prematur: ( -3.04, -0.63) T-Test mu FullTerm = mu Prematur (vs <): T= -3.16 P=0.0023 DF=22 Both use Pooled StDev = 1.42 Two Sample T-Test and Confidence Interval Two sample T for FullTerm vs Premature N Mean StDev SE Mean FullTerm 12 10.38 1.40 0.40 Prematur 12 12.21 1.45 0.42 95% CI for mu FullTerm - mu Prematur: ( -3.04, -0.63) T-Test mu FullTerm = mu Prematur (vs >): T= -3.16 P=1.0 DF= 22 Both use Pooled StDev = 1.42 |
(A) 0.0046 | (B) 0.0023 | (C) 1.0 | (D) -3.16 |
__E__ 14. Which, if any, of the following would be valid conclusions that the researchers could draw from these three sets of output? There is sufficient evidence to conclude that...
(i) premature babies walk, on average, at a later age than full term babies
(ii) premature babies walk, on average, at a different age than full term babies
(iii) premature babies walk, on average, at an earlier age than full term babies
(A) None | (B) Only (i) | (C) Only (ii) | (D) Only (iii) |
(E) (i) and (ii) | (F) (i) and (iii) | (G) (ii) and (iii) | (H) All |
Questions 15 and 16 pertain to the following situation.
Does sensory deprivation have an effect on a person's alpha-wave frequency?
Twenty volunteer subjects were randomly divided into two groups.
Subjects in group A were subjected to a 10-day period of sensory deprivation,
while subjects in group B served as controls. After the 10-day period,
the alpha-wave frequency component of subjects' electroencephalograms were
measured, and the following Minitab output generated:
Two Sample T-Test and Confidence Interval Two sample T for GrpB vs GrpA N Mean StDev SE Mean GrpB 10 11.080 0.459 0.15 GrpA 10 10.280 0.598 0.19 95% CI for mu GrpB - mu GrpA: ( 0.30, 1.30) T-Test mu GrpB = mu GrpA (vs not =): T= 3.36 P=0.0035 DF= 18 Both use Pooled StDev = 0.533 T-Test of the Mean Test of mu = 11.000 vs mu not = 11.000 Variable N Mean StDev SE Mean T P GrpA 10 10.280 0.598 0.189 -3.81 0.0042 GrpB 10 11.080 0.459 0.145 0.55 0.59 |
__B__ 15. What type of study did the researchers conduct?
(A) an observational study | (B) an experiment |
__A__ 16. Which of the following is the correct decision?
(A) P-value is 0.0035. Conclude that sensory deprivation does have an effect on a person's alpha-wave frequency.
(B) P-value is 0.0035. Conclude that sensory deprivation does not have an effect on a person's alpha-wave frequency.
(C) P-value is 0.0042. Conclude that sensory deprivation does have an effect on a person's alpha-wave frequency.
(D) P-value is 0.0042. Conclude that sensory deprivation does not have an effect on a person's alpha-wave frequency.
(E) P-value is 0.59. Conclude that sensory deprivation does have an effect on a person's alpha-wave frequency.
(F) P-value is 0.59. Conclude that sensory deprivation does not have an effect on a person's alpha-wave frequency.
Questions 17 to 18 pertain to the following set-up. The number of years a person lives after being diagnosed with a certain disease is normally distributed with a mean of 4 years and a standard deviation of 1 year.
17. What is the probability that a randomly selected individual with the disease will live more than 5.5 years?
18. What is the probability that a randomly selected individual will live between 3.5 and 5.2 years?