Suppose that 20 of a random sample of n = 64 men are currently single. What is the standard error of ...

Suppose that 20 of a random sample of n = 64 men are currently single. What is the standard error of the proportion of single men in the sample?
 a. 0.125
  b. 0.05
  c. 0.10
  d. 0.20

Q. 2

Random samples of 5 Japanese women and 10 Japanese men showed an average life span of 83 years for the women and 77 years for the men. The standard deviation was 2 years for the women and 1 year for the men. Calculate a 95 confidence interval for the difference in average life spans (women - men). Assume that the life spans are normally distributed, but do not assume the population variances are equal, and use the conservative by-hand estimate for the degrees of freedom.

Q. 3

Sleep apnea is a condition involving irregular breathing during sleep. Suppose that 20 of a population of men experience sleep apnea. A random sample of n = 64 men is to be drawn from this population. What is the mean of the sampling distribution for the sample proportion of men who experience sleep apnea?
 a. 20/64
  b. 0.20
  c. 0.80
  d. It depends on the value of the sample proportion.

Q. 4

For a randomly selected sample of 20 new mothers in the year 2000, the mean age was 24.6 years. For a randomly selected sample of 10 new mothers in 1970, the mean age was 21.4 years. The difference between the mean ages is 3.2 years, and the standard error of the difference is 1.366 . Assume that the ages of new mothers are normally distributed, do not assume the population variances are equal, and use the conservative by hand estimate for the degrees of freedom. Calculate a 99 confidence interval for the difference in population mean ages of new mothers in the two years (year 2000  year 1970).
 a. (1.24, 7.64)
  b. (1.13, 7.53)
  c. (0.47, 5.93)
  d. None of the above

Q. 5

Which one of the following statements is false?
 a. A sampling distribution is the probability distribution of a sample statistic. It describes how values of a sample statistic vary across all possible random samples of a specific size that can be taken from a population.
  b. For all five scenarios considered, the sampling distribution is approximately normal as long as the sample size(s) are large enough.
  c. The mean value of a sampling distribution is the mean value of a sample statistic over all possible random samples. For the five scenarios, this mean equals the value of the statistic.
  d. The standard deviation of a sampling distribution measures the variation between all possible values of the sample statistic and their mean over all possible random samples. For the five scenarios, this mean equals the value of the parameter.

Q. 6

For a randomly selected sample of 20 new mothers in the year 2000, the mean age was 24.6 years. For a randomly selected sample of 10 new mothers in 1970, the mean age was 21.4 years. The difference between the mean ages is 3.2 years, and the standard error of the difference is 1.366 . Assume that the ages of new mothers are normally distributed, do not assume the population variances are equal, and use the conservative by hand estimate for the degrees of freedom. Calculate a 90 confidence interval for the difference in population mean ages of new mothers in the two years (year 2000  year 1970).
 a. (0.84, 5.56)
  b. (0.78, 5.67)
  c. (0.70, 5.70)
  d. None of the above

Q. 7

Which one of the following statements is false?
 a. The standard error measures the variability of a population parameter.
  b. The standard error of a sample statistic measures, roughly, the average difference between the values of the statistic and the population parameter.
  c. Assuming a fixed value of s = sample standard deviation, the standard error of the mean decreases as the sample size increases.
  d. The standard error of a sample proportion decreases as the sample size increases.

Q. 8

Reaction time is measured in a driving simulator for a random sample of 16 year-old boys (n = 12, = 4.5, s = 1.1) and a random sample of 24 year-old young men (n = 9, = 2.9, s = 1.3). Calculate a 99 pooled confidence interval for the difference in mean reaction time (16 year-olds  24 year-olds).
 a. (0.48, 2.72)
  b. (0.51, 2.70)
  c. (0.07, 3.13)
  d. None of the above