Q1. Assume that two independent random samples of size 100 each are taken from a population that has a variance of 36. What is the probability that the difference in the sample means is less than 2?
A. 0.4909
B. 0.9909
C. 0.0091
D. 0.5091
Q2. A random sample of 36 items is taken from a population which has a population variance of 144. The resulting sample mean is 45. A random sample of 36 items is taken from a population which has a population variance of 121. The resulting sample mean is 49. Using this information, calculate a 98% confidence interval for the difference in means of these two populations.
A. -10.99 to 2.99
B. -10.32 to 2.32
C. -8.46 to 0.46
D. -9.32 to 1.32
Q3. Lucy Baker is analysing demographic characteristics of two television programs, McLeod's Daughters (population 1) and 60 Minutes (population 2). Previous studies indicate no difference in the ages of the two audiences. (The mean age of each audience is the same.) Her staff randomly selected 100 people from each audience, and reported the following: x1‾= 43 years and x2‾ = 45 years. Assume that σ1 = 5 and σ2 = 8. Assuming a two-tail test and α = .05, the observed z-value is ____________.
A. -2.12
B. -2.25
C. -5.58
D. -15.38
Q4. In testing a hypothesis about two population means, if the t-distribution is used, we must assume _______.
A. the sample sizes are equal
B. the population means are the same
C. the standard deviations are not the same
D. both populations are normally distributed
Q5. A researcher wishes to determine the difference in two population means. To do this, she randomly samples 9 items from each population and calculates a 90% confidence interval. The sample from the first population produces a mean of 780 with a standard deviation of 240. The sample from the second population produces a mean of 890 with a standard deviation of 280. Assume that the values are normally distributed in each population. The point estimate for the difference in the means of these two populations is _______.
A. -110
B. 40
C. -40
D. 0