- (B) Because is an unbiased estimator of the mean, the sampling distribution of those sample means
has the same value as the population. Therefore mean = 210. The standard deviation of the sampling
distribution is given by = 3.75. However, the population is substantially skewed right
and the sample size is very small. Therefore we cannot say that the shape of the sampling distribution
is approximately normal.
- (B) The z -score for the first quartile (p = 0.25) is −0.674. . So
- (E) The correct option provides the explanation.
- (C) The question asks which is least likely to reduce bias in a sample survey. Simple random
sampling is unbiased, so using a stratified random sample would not improve on that. You can take a
representative sample but still introduce bias unless you address the actions in choices (A), (B), (D),
and (E).
- (B) Degrees of freedom are calculated by (rows − 1)(columns − 1). In this case, (5 − 1)(2 − 1) = 4
- (C) This can be done using a two-way table.
The required probability is 0.0049/0.03475 = 0.1410
- (E) That is the definition of power.
- (C) The number of successes and failures each needs to be greater than 10 for both males and
females. Since the success/failure numbers for females are 66/4, we do not meet this condition.
- (D) We did not change the significance level, which is the probability of making a Type I error.
Increasing the sample size is one way to increase the power of the test.
- (C) Each volunteer behaves as his or her own block. Therefore, a matched pairs test is appropriate.
- (A) This choice correctly interprets the confidence level of 95%. When you take many, many, many
samples of the same size, 95% of the confidence intervals you build around your sample results will
contain the parameter you hope to estimate.
- (B) Since zero is contained in the interval, zero (representing no difference in the means) is a
plausible value. So, we do not have convincing evidence that there is a difference.
