STAT 2430 Unit7B HW(1)
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Feb 20, 2024
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UNIT 7B HOMEWORK SET
8 Points Possible
In this homework set we will explore working with confidence intervals for means in more depth. Please respond with complete sentences as appropriate. You must show your work for full credit. You will lose points if work is not shown, even if the answer is correct.
(1) A confidence interval for the price of gasoline from a random sample of 30 gas stations in a region gives the following statistics (2 points):
X
=
3.91
, SE
(
X
)
=
0.12
a) Find the 95% confidence interval for the mean gasoline price in the region:
b) Now find the 90% confidence interval for the mean:
c) If we had the same statistics with a sample of 60 gas stations in the region, what would the 95% confidence interval with new n be?
(2) A credit card company takes a random sample of 100 cardholders to see how much they charged on their card last month. A histogram and boxplot are below:
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A computer program found that the 95% confidence interval for the mean amount spent in January 2020 is ($6472.86, $172,328.44). Explain why the analysts did not find this interval useful and indicate what went wrong (2 points).
(3) While reviewing a sample of audit fees, a senior accountant for a tax firm notes that the fee charged by the firm’s accountants depends on the complexity of the return. A comparison of actual charges therefore might not
provide the information needed to set next year’s fees. To better understand
the fee structure, the senior accountant requests a new sample that measures the time the accounts spent on each audit. Last year, the mean hours charged per client was 3.7 hours. A new sample of 15 audit times shows the following times in hours (1 point):
4.2, 3.7, 4.1, 4.8, 2.9, 2.7, 3.1, 4.5, 4.0, 4.2, 4.0, 4.1, 5.0, 3.4, 3.5
a) Assume assumptions and conditions have been met. What is the 90% confidence interval for the mean audit time?
b) Do you think audit times have, in fact, increased?
YES
NO
EXPLAIN YOUR CHOICE:
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(4) Hoping to lure more shoppers downtown, a city builds a new public parking garage in the central business district. The city plans to pay for the structure through parking fees. For a random sample of 52 weekdays, daily feels collected averaged $125 with a standard deviation of $16 (2 points)
(a) What is the 99% confidence interval for the mean daily income this parking garage will generate?
(b) Interpret this confidence interval in context:
(c) The consultant who advised the city on this project predicted that parking revenues would average $150 dollars per day. Based on your confidence interval, what do you think of the consultant’s prediction? Why?
(d) Would a 90% confidence interval support the consultant’s prediction? Calculate the 90% confidence interval and discuss your results.
(5) How far do professional golfers drive a ball? (For non-golfers, the drive is the shot hit from a tee at the start of a hole and is typically the longest shot).
Below is a histogram of the driving distances for 207 players in the 2019 U.S.
Open tournament along with summary statistics (1 point).
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Mean = 292.5 yards
SD = 8.5 yards
n = 207
(a) Find a 95% confidence interval for the mean drive distance:
(b) Interpret this interval in context: