Brief Solutions to Practice Final Examination

Problem 1
(a) z = 0.98; area = 0.1635.
(b) z = 1.69; area = 0.0455
(c) 124.031

Problem 2
(a) Active group: Q1 = 21, M = 23.5, Q3 = 28; Passive group: Q1 = 15, M = 17, Q3 = 20.5.
(b) In the Active group, 44 is an outlier by the 1.5 IQR rule.; There are no outliers in the Passive group.
(c) The Active group is skewed somewhat to the right.
(d) It looks as if the active group did better. The distribution is shifted to the right relative to the Passive group.
(e) Yes, the test statistic is much larger than 2.426.

Problem 3
(a) The mean is 24.4. The standard deviation is 6.3.
(b) 24.4 +/- 2.069*(6.3/sqrt(24)), or 24.4 +/- 2.7.
(c) t = 3.42. The p-value is between 0.001 and 0.0025.
(d) There is very strong evidence that active learning resulted in higher test scores, and that the observed difference is not easily explained by regular chance variation.

Problem 4
(a) There is a positive association.
(b) The relationship is very strong. The correlation coefficient is nearly one.
(c) (estimated absorbance) = 1.66 + 0.113(nitrate level)
(d) The residual is 93 - (1.66+0.113*800) = 0.94
(e) Estimate is 58.3. I expect it to be accurate.
A plot shows the relationship is very close to being perfectly linear, as is also indicated by the high r value.

Problem 5
(a) X may be modeled as binomial because:
There is a fixed sample size (600);
Each ballot either registered a vote or did not (two possible outcomes);
The ballots are independent (approximately, since n is much smaller than the population size);
Each ballot has the same chance of (0.015) of having not registered a vote.

Problem 6

Problem 7
False, correlation coefficients do not have units (inches).

Problem 8

Problem 9
False, sampling distributions of small samples from non-normal populations may not be normal.

Problem 10
False, it should be 1000!/(500!500!).

Problem 11
False, there are some random samples that are not simple where each individual has the same chance of being selected (for example, stratified random samples from equal size strata).

Problem 12
False, the p-value is not the probability that the null hypothesis is true.

Problem 13
False, a 95% confidence interval for mu describes the location of mu, not the location of the middle 95% of the population.

Problem 14
False, it would not be significant at the 5% level.

Problem 15
False, when a test is not significant it does not mean that the null hypothesis is true. Also, a test can be not significant when the sample test statistic is not exactly the population parameter value.