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For questions 8-10, provide a screenshot of R analysis results.
1. The heights of North American women are normally distributed with a mean of 64 inches and a
standard deviation of 2 inches.
a. What is the probability that a randomly selected woman is taller than 66 inches?
b. A random sample of four women is selected. What is the probability that the sample mean
height is greater than 66 inches?
c. What is the probability that the mean height of a random sample of 100 women is greater than
66 inches?
2. The Laurier Company’s brand has a market share of 30%. Suppose that in a survey 1000
consumers of the product are asked which brand they prefer. What is the probability that more than
32% of the respondents say they prefer the Laurier brand?
3. A sample of 15 workers reveals the following number of minutes spent traveling.
29, 38, 38, 33, 38, 21, 45, 34, 40, 37, 37, 42, 30, 29, 35
Develop a 95 percent confidence interval for the population mean. Interpret the result.
4. An economist is interested in studying the incomes of consumers in a particular region. The
population standard deviation is known to be $1,000. What sample size would the economist need
to use for a 95% confidence interval if the difference between UCL and LCL should not be more
than $100?
5. Huntington National Bank installed an ATM. After several months of operation, a sample of 100
customers reveals the following use of the ATM in a month.
Number of Times ATM Used Frequency
0 25
1 30
2 20
3 10
4 10
5 5
a. What is the estimate of proportion of customers who do not use the ATM in a month?
b. Develop 95 percent confidence interval for this estimate. Can the bank be sure that at least 40%
of customers will use the ATM?
6. The MacBurger restaurant chain claims that the mean waiting time of customers is 3 minutes with
a population standard deviation of 1 minute. The quality assurance department found in a sample of
50 customers that the mean waiting time was 2.75 minutes. At the 0.05 significance level, can we
conclude that the mean waiting time is less than 3 minutes?
H0:
H1:
Critical Value
Test Statistics
p-value
Decision
7. A company claims that 10% of the users of a certain allergy drug experience drowsiness. In clinical
studies of this allergy drug, 81 of the 900 subjects experienced drowsiness
a. We want to test their claim and find out whether the actual percentage is not 10%. State the
appropriate null and hypotheses.
b. Is there enough evidence at the 5% significance level to infer that the competitor is correct?
c. Compute the p-value of the test.
d. Construct a 95% confidence interval estimate of the population proportion of the users of this
allergy drug who experience drowsiness.
e. Explain how to use this confidence interval to test the hypotheses.
8. Refer to the “wool.csv” file, which includes 54 observations on three variables.
Breaks: The number of breaks
Wool: The type of wool (A or B)
Tension: The level of tension (L, M, H)
Use R software to answer the following questions.
a. At the 5% significance level, is there sufficient evidence to infer that the mean number of
breaks is 30?
b. At the 5% significance level, is there sufficient evidence of a difference in the mean number of
breaks between two wool types A and B?
c. At the 5% significance level, is there sufficient evidence of a difference in the mean number of
breaks among three tension levels (L, M, H)?
9. A new equipment was recently installed. The manager would like to know if the mean processing
time using the new equipment is shorter than that using the old equipment. She gathered the
following sample information.
New equipment 4.5, 8.1, 5.9, 3.7, 7.2, 5.4, 5.7, 6.6
Old equipment 6.7, 7.0, 6.4, 7.3, 6.8, 6.9, 7.0, 6.6, 7.1, 6.8, 6.7, 6.8, 6.6
The manager first conducted hypothesis test for equality of two variances in which the null
hypothesis is that two populations have the same variance. The test results are given as follows.
F test to compare two variances
data: x1 and x2
F = 35.4081, num df = 7, denom df = 12, p-value = 8.742e-07
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
9.817806 165.207978
sample estimates:
ratio of variances 35.40806
At the 0.05 significance level, can we conclude that there is no change in the mean processing time?
Use R software to answer this question.
10. To compare the wearing of two types of automobile tires, 1 and 2, an experimenter chose to "pair"
the measurements, comparing the wear for the two types of tires on each of 7 automobiles, as
shown below.
Automobile 1 2 3 4 5 6 7
Tire 1 8 15 7 9 10 13 11
Tire 2 12 18 8 9 12 11 10
Determine whether these data are sufficient to infer at the 10% significance level that the two types
of tires wear differently.
Use R software to answer this question.