Statistics DC: Spring Semester Final Exam Review
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Name:___________________________________________
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Do you try to pad an insurance claim to cover your deductible? About 40% of all U.S. adults will try to pad their
insurance claims! Suppose that you are the director of an insurance adjustment office. Your office has just received 128
insurance claims to be processed in the next few days. Check if you can use the normal approximation, then find the
probability that
(a) Half or more of the claims have been padded?
(b) Fewer than 45 of the claims have been padded?
(c) From 40 to 64 of the claims have been padded?
(d) More than 80 of the claims have not been padded?
6.
A recent Harris Poll on green behavior showed that 25% of adults often purchase used items instead of new ones.
Consider a random sample of 75 adults. Let 𝑝̂ be the sample proportion of adults who often purchase used instead of
new items.
(a) Is it appropriate to approximate the 𝑝̂ distribution with a normal distribution? Check.
(b) What are the values of 𝜇𝑝̂ and 𝜎𝑝̂ ?
7.
The personnel office at a large electronics firm regularly schedules job interviews and maintains records of the
interviews. From the past records, they have found that the length of a first interview is normally distributed, with mean
35 minutes and standard deviation 7 minutes.
(a) What is the probability that a first interview will last 40 minutes or longer?
(b) Nine first interviews are usually scheduled per day. What is the probability that the average length of time for
nine interviews will be 40 minutes or longer?
(c) Comment on the difference between results (a) and (b), using the central limit theorem.
8. As part of an environmental studies class project, students measured the circumferences of a random sample of 45
blue spruce trees near Brainard Lake, Colorado with a sample mean circumference was 29.8 inches. Assuming the
standard deviation is known to be 7.2 inches. Find a 95% confidence interval for the population mean circumference of
all blue spruce trees near this lake. Interpret in context.
9. Collette is self-employed and sells cookware at home parties. She wants to estimate the average amount a client
spends at each party. A random sample of 35 receipts gave a mean of $34.70 with standard deviation $4.85.
(a) Find a 90% confidence interval for the average amount spent by all clients.
(b) What conditions are necessary for your calculations?
(c) For a party with 35 clients, use part (a) to estimate a range of dollar values for Collette’s total sales at that
party.
10. A random sample of 78 students was interviewed, and 59 students said that they would vote for Jennifer McNamara
as student body president.
(a) Let p represent the proportion of all students at this college who will vote for Jennifer. Find a point estimate
for p and q.
(b) Find a 90% confidence interval for p.
(c) What assumptions are required for the calculations of part (b)? Are they satisfied?
11. How long does it take to commute from home to work? It depends on several factors, including route, traffic, and
time of departure. The data below are results (in minutes) from a random sample of eight trips. Use these data to create
a 95% confidence interval for the population mean time of the commute. (use calculator)
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38
30
42
24
37
30
39
12. A random sample of 19 rainbow trout caught at Brainard Lake, Colorado, had a mean length of 11.9 inches with a
standard deviation of 2.8 inches. Find a 99% confidence interval for the population mean length of all rainbow trout in
this lake. Interpret in context.
13. A random sample of 53 students was asked for the number of semester hours they are taking this semester. The
sample standard deviation was found to be 4.7 semester hours. How many more students should be included in the
sample to be 99% confident that the sample mean is within 1 semester hour of the population mean for all students at
this college?
14. What percentage of college students owns a cellular phone? Let p be the proportion of college students that owns a
cellular phone.
(a) How large a sample is needed to be 90% confident that a point estimate will be within a distance of 0.08
from p?
(b) If a previous study showed approximately 38% of college students own cellular phones, answer part (a)
using this estimate for p.
15. How long do new batteries last on a camping trip? A random sample of 42 small camp flashlights were fitted with
brand 1 batteries and left on until the batteries failed. The sample mean lifetime was 9.8 hours. Another random sample
of 38 small flashlights of the same model were fitted with brand 2 batteries and left on until the batteries failed. The
sample mean of lifetimes was 8.1 hours. Past experience suggests the standard deviation of brand 1 lifetimes was 2.2
hours and standard deviation of brand 2 lifetimes was 3.5 hours. Find a 90% confidence interval for the population
difference of lifetimes for these batteries. Interpret with context.
16. Two pain-relief drugs are being considered. A random sample of 8 doses of the first drug showed that the average
amount of time required before the drug was absorbed into the bloodstream was 24 minutes with standard deviation 3
minutes. For the second drug, a random sample of 10 doses showed the average time required for absorption was 29
minutes with standard deviation 4.9 minutes. Assume that the absorption times are normal. Find a 90% confidence
interval for the difference in average absorption times for the two drugs. Interpret with context.
17. A random sample of 83 investment portfolios managed by Kendra showed that 62 of them met the targeted annual
percent growth. A random sample of 112 portfolios managed by Lisa showed that 87 met the target annual percent
growth. Find a 99% confidence interval for the difference in the proportion of the portfolios meeting target goals
managed by Kendra compared with those managed by Lisa. Interpret with context.
18. A large furniture store has begun a new ad campaign on local television. Before the campaign, the long-term average
daily sales were $24,819. A random sample of 40 days during the new ad campaign gave a sample mean daily sale
average of $25,910. From past experience, the daily sales had a standard deviation of $1917. Does this indicate that the
population mean daily sales are now more than $24,819? Use α =0.01.
19. A music teacher knows from past records that 60% of students taking summer lessons play the piano. The instructor
believes that this proportion may have dropped owing to the popularity of wind and brass instruments. A random
sample of 80 students yielded 43 piano players. Test the instructor’s claim at a α = 0.05 level.
20. How long does it take to have food delivered? A Chinese restaurant advertises that the average delivery time will be
more than 30 minutes. A random sample of delivery times (in mins) is showed below. Based on this sample, is the
average delivery time greater than 30 minutes? Use α = 0.05.
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28
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39
30
27
29
39
32
28
42
25
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30
21. How tall are college hockey players? The average height has been 68.3 inches. A random sample of 14 hockey
players gave a mean height of 69.1 inches. We may assume that standard deviation of heights is 0.9 inches. Does this
indicate that the population mean height is different from 68.3 inches? Use α = 0.05
22. A systems specialist studied the workflow of clerks doing the same inventory work. Based on this study, she
designed a new workflow layout for the inventory system. To compare average production for the old and new
methods, six clerks were randomly selected for the study. The average production rate for each clerk was recorded
before and after the new system was introduced. The results are shown below. Test the claim that the new system
increases the mean number of items process per shift. Use α = 0.05.
23. How productive are employees? One way to answer this question is to study annual company profits per employee.
A random sample of 11 computer stores gave a mean of 25.2 thousand dollars profit per employee with a standard
deviation of 8.4 thousand dollars. Another random sample of 9 building supply stores in St. Louis gave a mean of 19.9
thousand dollars per employee with standard deviation of 7.6 thousand dollars. Does this indicate that in St. Louis,
computer stores tend to have higher mean profits per employee? Use α = 0.01.
24. Do organic farming methods cause a chance in produce size? A random sample of 89 organically grown tomatoes
had mean weight 3.8 ounces. Another random sample of 75 tomatoes that were not grown organically had a mean of
4.1 ounces. Previous studies show that the standard deviation for the organically grown tomatoes was 0.9 ounce and for
the non-organic grown tomatoes it was 1.5 ounces. Does this indicate a difference between population mean weights of
organically grown tomatoes compared with those not grown organically? Use α = 0.05.
25. For communities in western Kansas, the rate of hay fever per 1000 population was collected for a random sample of
16 communities for people under 25 years old , and another random sample of 14 communities for people over 50. The
results are shown below:
Under 98
90
120 128 92
123 112 93
125 95
125 117 97
122 127 88
25
Over
95
110 101 97
112 88
110 79
115 100 89
114 85
96
50
Does the data indicate that the age group over 50 has a lower rate of hay fever? Use α = 0.05.
26. A telemarketer is trying two different sales pitches to sell a carpet cleaning service. For his aggressive sales pitch, 175
people were contracted by phone, and 62 of those people bought the cleaning service. For his passive sales pitch, 154
people were contacted by phone, and 45 of those people bought the cleaning service. Does this indicate that there is
any difference in the population proportions of people who will buy the cleaning service depending on which sales pitch
is use? Use α = 0.05.
Also study: Quiz 6.4/6.5
Quiz 7.1-7.3
Quiz 7.4
Quiz 8.1-8.3
Quiz 8.4/8.5
Quiz 9.1-9.3 (Regression WILL be on the final!)
Review notes from second semester (6.4 and on) because any theory is also fair
game!