Chapter 8.
Sampling Distribution and Estimations
Q1. The Ball Corporation’s beverage can manufacturing plant in Fort Atkinson, Wisconsin, uses a
metal supplier that provides metal with a known thickness standard deviation σ = .000959 mm. If a
random sample of 58 sheets of metal resulted in x = 0.2731 mm, calculate the 99 percent confidence
interval for the true mean metal thickness.
Q2. A sample of 21 minivan electrical warranty repairs for “loose, not attached” wires (one of several
electrical failure categories the dealership mechanic can select) showed a mean repair cost of $45.66
with a standard deviation of $27.79. Construct a 95 percent confidence interval for the true mean
repair cost.
Q3. A survey showed that 4.8 percent of the 250 Americans surveyed had suffered some kind of
identity theft in the past 12 months. (a) Construct a 99 percent confidence interval for the true
proportion of Americans who had suffered identity theft in the past 12 months. (b) May normality of p
be assumed? Explain.
Q4. In an intra-squad swim competition, men’s freestyle 100 swim times at a certain university
ranged from 43.89 seconds to 51.96 seconds. (a) Estimate the standard deviation using Method 3 (the
Empirical Rule for a normal distribution). (b) What sample size is needed to estimate the mean for all
swimmers with 95 percent confidence and an error of ±0.50 second?
Q5. Inspection of a random sample of 19 aircraft showed that 15 needed repairs to fix a wiring
problem that might compromise safety. How large a sample would be needed to estimate the true
proportion of jets with the wiring problem, with 90 percent confidence and an error of ±6 percent?
Chapter 9. One-Sample Hypothesis Tests
Q6. GreenBeam Ltd. claims that its compact fluorescent bulbs average no more than 3.50 mg of
mercury. A sample of 25 bulbs shows a mean of 3.59 mg of mercury. (a) Write the hypotheses for a
right-tailed test, using GreenBeam’s claim as the null hypothesis about the mean. (b) Assuming a
known standard deviation of 0.18 mg, calculate the z test statistic to test the manufacturer’s claim. (c)
At the 1 percent level of significance (α = .01) does the sample exceed the manufacturer’s claim? (d)
Find the p-value.
Q7. The average age of a part-time seasonal employee at a Vail Resorts ski mountain has historically
been 37 years. A random sample of 25 part-time seasonal employees in 2010 had a sample mean age
of 38.5 years with a sample standard deviation equal to 16 years. (a) At the 10 percent level of
significance, does this sample show that the average age was different in 2010? (b) Find p-value. (c)
Construct 90 percent confidence interval and verify the conclusion in (a).
Q8. To encourage telephone efficiency, a catalog call center issues a guideline that at least half of all
telephone orders should be completed within 2 minutes. Subsequently, a random sample of 64
telephone call orders showed that 24 calls lasted 2 minutes or less. Does this sample show that fewer
than half of all orders are completed within 2 minutes at 5 percent level of significance? (a) State the
appropriate hypotheses assuming π is the proportion of all calls that are completed within 2 minutes.
(b) Find the p-value. (c) Is it safe to assume normality of the sample proportion p?
Chapter 10. Two-Sample Hypothesis Tests
Q9. Is there a difference in the average number of years’ seniority between returning part-time
seasonal employees and returning full-time seasonal employees at a ski resort? From a random sample
of 191 returning part-time employees, the average seniority, 𝑥1 , was 4.9 years with a standard
deviation, 𝑠1 , equal to 5.4 years. From a random sample of 833 returning full-time employees, the
average seniority, 𝑥2 , was 7.9 years with a standard deviation, 𝑠2 , equal to 8.3 years. Assume the
population variances are not equal. (a) Test the hypothesis of equal means using α = .01. (b) Calculate
the p-value. (c) Construct a 99 percent confidence interval for the difference of tow means, 𝜇1 − 𝜇2 ,
and verify the conclusion in (a).
Q10. The average mpg usage for a 2017 Toyota Prius for a sample of 10 tanks of gas was 45.5 with a
standard deviation of 1.8. For a 2017 Ford Fusion, the average mpg usage for a sample of 10 tanks of
gas was 42.0 with a standard deviation of 2.3. (a) Assuming equal variances, at α = .01, is the true
mean mpg lower for the Ford Fusion? (b) Calculate the p-value.
Q11. Blue Box is testing a new “half price on Tuesday” policy on DVD rentals at a sample of 10
locations. (a) At α = .10, do the data show that the mean number of Tuesday rentals has increased? (b)
Is the decision close? (c) Are you convinced?
Q12. A survey of 100 mayonnaise purchasers showed that 65 were loyal to one brand. For 100 bath
soap purchasers, only 53 were loyal to one brand. Perform a two-tailed test comparing the proportion
of brand loyal customers at α = .05.
Q13. Examine the data below showing the weights (in pounds) of randomly selected checked bags for
an airline’s flights on the same day. (a) At α = .05, is the mean weight of an international bag greater?
Show the hypotheses, decision rule, and test statistic. (b) At α = .05, is the variance greater for bags on
an international flight? Show the hypotheses, decision rule, and test statistic.
Chapter 11. Analysis of Variance (ANOVA)
Q14. Refer to the following partial ANOVA results from a statistical software (some information is
missing).
(a) Fill in the missing values.
(b) Find the number of observations.
(c) Find the number of treatment groups.
Chapter 12. Simple Regression
Q15. Given the following table,
a) Calculate the correlation coefficient.
b) Find critical values for a two-tailed test at α = .05.
c) Calculate the t test statistic. Can you reject ρ = 0 at α = .05?
d) Write the fitted regression using OLS.
e) If the number of orders increases by 100, how much would the expected Ship Cost increase?
Q16. A researcher's results are shown below using n = 25 observations.
(a) Construct 95 percent confidence interval for the slope.
(b) Construct 95 percent confidence interval for the intercept.
