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If the p-value of a test yields p = 0.3879, one would: | Complete Solution
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Round final answers to two decimal places.  α = 0.05 unless otherwise specified.

The numbers in (#) are the number of points for that question.  There are a total of 85 points for this exam.

Again, please write answers in BOLD.  If it is a multiple choice question, please highlight the correct answer.  If requested to answer in prose, use 20 words or less, (we only look at the first 20 words for the answer).  These answers need not be in full sentences, bullets are acceptable.

Symbols you may need to cut and paste into your answers:  χ2 μ 2  ± √ ≥ ≤ β α Φ

1.  (2) If the p-value of a test yields p = 0.3879, one would:

a.  reject the null

b.  not reject the null

c.  not enough information to answer the question

2.  (2) You are reading an article detailing a study designed to compare the average body mass index among hypertensive individuals (persons with high blood pressure) to normotensive individuals.  The study was conducted using participants in a health plan offered by a large insurance carrier.  Two-hundred randomly selected hypertensive participants were compared to 200 randomly selected normotensive participants.  The study reports a 95% CI of (0.15 kg/m2, 2.43 kg/m2) for the difference in the mean BMI between hypertensive and normotensive individuals.  However, no p-value was reported for the test of the null hypothesis of no mean difference in BMI between the two groups.  Which of the follow is true?

a.  The p-value is <0.05

b.  The p-value is > 0.05

c.  The p-value is = 0.05

d.  The p-value is = 0.15

3.  (2) Suppose you are testing H0: μ1 = μ2 + 3 vs. HA:  μ1 ≠  μ2 + 3 and the resulting confidence interval calculated for μ1 - μ2 is (1.03,3.27):

a.  The resulting p-value of the test of hypothesis would reject the null

b.  the resulting p-value of the test of hypothesis would not reject the null

c.  the resulting p-value of the test of hypothesis would be inconclusive

d.  none of the above

4  (2) What is the test statistic value for testing the null hypothesis that the population mean is 27?

a.  t = 3.98

b.  t = -3.98

c.  t = 4.6

d.  t = -4.6

e.  t = 1.96

5.  (8) For each obtained value stated below: (1) What is the decision for each if α = .05 (one tailed test, upper tail)? (2) What is the decision for each if α = .10 (two tailed test)?  Circle the correct answers for (1) and (2)

(1)                                (2)

a.  p = 0.07            reject/do not reject      reject/do not reject

b.  p = 0.70            reject/do not reject      reject/do not reject

c.  p = 0.04            reject/do not reject      reject/do not reject

d.  p = 0.53            reject/do not reject      reject/do not reject

6.  (2) A study looked at the number of additional cavities in children before and after public water fluoridation projects in 54 North American cities.  This appropriate test of hypothesis to use is:

a.  independent one-sample t-test of the means

b.  independent two-sample t-test of the means

c.  one-sample χ2 test of the variance

d.  two-sample χ2 test of the variances

e.  paired t-test of the mean difference

f.  none of the above

7.  In a study of maternal exposure to trihalomethanes in the drinking water in the first trimester of pregnancy and infant birth weight, the birth weight of infants born to exposed women in a cohort of over 6,000 births will be compared to the state average.  The study was looking for evidence that exposure to trihalomethanes in drinking water in the first trimester of pregnancy decreases birth weight.

a.  (2)  If the resulting 95% one-sided CI about the mean is (-∞g, 3498g), would we reject or not reject a test of a null hypothesis of equality with the state average of 3315g?  Explain your answer.

8.  Calcium is normally present in mammalian blood in concentrations of about 6 mg per 100 mL of whole blood.  The normal standard deviation of this variable is 1 mg of calcium per 100 mL of whole blood.  Variability larger than this can lead to severe disturbances in blood coagulation.  A series of nine tests on a patient revealed a sample mean of 6.2 mg per 100 mL of whole blood and a sample s.d. of 1.40.  Use α = .10.

a.  (2) What is the outcome variable of concern?

b.  (2) What is the measurement scale of the outcome variable?

c.  (2) What is the null hypothesis?  (In prose)

d.  (3) Is there cause for concern about blood coagulation in this patient?

e.  (3) Calculate a 90% confidence interval about σ2.  Is there cause for concern?

f.  (3) Explain the similarities and differences between the results in part d and in part e.

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