2. Your statistics instructor wants you to determine a confidence interval estimate for the
mean test score for the next exam. In the past, the test scores have been normally
distributed with a mean of 74.2 and a standard deviation of 30.9. A 95% confidence
interval estimate if your class has 30 students is: (Points: 2) A) 68.72 to 79.68 B) 13.64 to
134.76 C) 64.92 to 83.48 D) 63.14 to 85.26
Answer: D) 63.14 to 85.26
The 95% confidence interval is
(xbar – 1.96*σ/√n, xbar + 1.96*σ/√n)
= (74.2 – 1.96*30.9/√30, 74.2 + 1.96*30.9/√30)
= (63.14, 85.26)
3. A random sample of size 15 taken from a normally distributed population revealed a
sample mean of 75 and a sample variance of 25. The upper limit of a 95% confidence
interval for the population mean would equal: (Points: 2) A) 77.769 B) 72.231 C) 72.727
D) 77.273
Answer: A) 77.769
Upper limit = xbar + t*s/√n = 75 + 2.145*5/√15 = 77.769
4. You are interested in determining the average cost of a 3-minute telephone call to
locations within the continental U.S. What sample size must you take to be 96%
confident that the results will be within $.75 of the true mean cost per call? From the
phone company, you have gotten an estimate of = 7.71. (Points: 2) A) 185 B) 445 C) 406
D) 574
Answer: B) 445
n = (z*σ/E)^2 =[(2.054*7.71)/0.75]^2 = 445
5. The Arkansas State Police wish to estimate the average mph being traveled on the
Interstate Highways, which cross the state. If the estimate is to be within 8 mpg of the
true mean with 98% confidence and the estimated standard deviation is 22 mph, how
large a sample size must be taken? (Points: 2) A) 42 B) 15 C) 329 D) 14
Answer: A) 42
n = (z*σ/E)^2 =[(2.326*22)/8]^2 = 42
7. A professor of math refutes the claim that the average student spends 3 hours studying
for the midterm exam. Which hypothesis is used to test the claim? (Points: 2) H0: 3, H1:
> 3 H0: = 3, H1: 3 H0: 3, H1: = 3 H0: = 3, H1: < 3
Answer: H0: μ =3, H1: μ ≠ 3
8. Which of the following p-values will lead us to reject the null hypothesis if s = 0.05?
(Points: 2) A) 0.15 B) 0.10 C) 0.05 D) 0.025
Answer: D) 0.025
If p-value < 0.05 we reject Ho.
9. A mortgage broker is offering home mortgages at a rate of 9.5% but is fearful that this
value is higher than many others are charging. A sample of 40 mortgages filed in the
county court house shows an average of 9.25% with a standard deviation of 8.61%. Does
this sample indicate a smaller average? Use s = 0.05 and assume a normally distributed
population. (Points: 2) A) Yes, the test statistic falls in the rejection region. B) No, the
test statistic falls in the acceptance region. C) Yes, because the test statistic is greater than
-1.645. D) No, because the test statistic is -1.85 and falls in the rejection region.
Answer: B) No, the test statistic falls in the acceptance region.
Here the test statistic t = (xbar – 9.5)/ s/√n = (9.25 -9.5)/(8.61/√40) = -0.1836
The critical value = - 1.645
The decision rule is reject Ho if t < - 1.645
Here t = -0.1836 > -1.645
Thus the test statistic falls in the acceptance region.
10. The power of a test is the probability of making: (Points: 2) A) a correct decision
when the null hypothesis is false B) a correct decision when the null hypothesis is true C)
incorrect decision when the null hypothesis is false D) incorrect decision when the null
hypothesis is true
Answer: A) a correct decision when the null hypothesis is false