Find the value of x such that P(t 10 > x) = 0.75, where t 10 has a t distribution with 10 degrees of freedom

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distribution with 100 degrees of
freedom. How do you explain the difference between this result and the result obtained in part a?
c. Find the value of z such that P(Z > z) = 0.75, where Z is a standard normal random variable. Compare this
result to the results obtained in parts a and b. How do you explain the differences in the values of x, y, and
z?
6. The file P08_06.xlsx contains data on repetitive task times for each of two workers. John has been
doing this task for months, whereas Fred has just started. Each time listed is the time (in seconds) to
perform a routine task on an assembly line. The times shown are in chronological order.
a. Calculate a 95% confidence interval for the mean time it takes John to perform the task. Do the same for
Fred.
7. The manager of a local fast-food restaurant is interested in improving the service provided to
customers who use the restaurant’s drive-up window. As a first step in this process, the manager asks an
assistant to record the time (in seconds) it takes to serve a large number of customers at the final
window in the facility’s drive-up system. The file P08_07.xlsx contains a random sample of 200 service
times during the busiest hour of the day.
b) Calculate and interpret a 95% confidence interval for the mean service time of all customers arriving
during the busiest hour of the day at this fast-food operation.
15. A drugstore manager needs to purchase adequate supplies of various brands of toothpaste to meet
the ongoing demands of its customers. In particular, the company is interested in estimating the
proportion of its customers who favor the country’s leading brand of toothpaste, Crest. The Data sheet
of the file P08_15 .xlsx contains the toothpaste brand preferences of 200 randomly selected customers,
obtained recently through a customer survey. Calculate a 95% confidence interval for the proportion of
all of the company’s customers who prefer Crest toothpaste. How might the manager use this
confidence interval for purchasing decisions?
17. The employee benefits manager of a large public university would like to estimate the proportion of
full-time employees who prefer adopting the first (plan A) of three available health care plans in the next annual enrollment period. A random sample of the university’s employees and their tentative health
care preferences are given in the file P08_17.xlsx.
a. Calculate a 90% confidence interval for the proportion of all the university’s employees who favor plan A.
32. Elected officials in a California city are preparing the annual budget for their community. They would
like to estimate how much their constituents living in this city are typically paying each year in real
estate taxes. Given that there are over 100,000 homeowners in this city, the officials have decided to
sample a representative subset of taxpayers and study their tax payments.
a. What sample size is required to generate a 95% confidence interval for the mean annual real estate tax
payment with a half-length of $100? Assume that the best estimate of the population standard deviation σ
is $535.
c. Now suppose that the officials want to construct a 95% confidence interval with a half-length of $75.
What sample size is required to achieve this objective?
34. You are trying to estimate the average amount a family spends on food during a year. In the past the
standard deviation of the amount a family has spent on food during a year has been approximately
$1000. If you want to be 99% sure that you have estimated average family food expenditures within $50,
how many families do you need to survey?
24. A real estate agent has collected a random sample of 75 houses that were recently sold in a suburban
community. She is particularly interested in comparing the appraised value and recent selling price of
the houses in this particular market. The data are provided in the file P08_24.xlsx. Using this sample
data, calculate a 95% confidence interval for the mean difference between the appraised values and
selling prices of the houses sold in this suburban community. Interpret the confidence interval for the
real estate agent.
Include your interpretation in blank cell under the calculations and output.