STAT 1342 - Exam Two
Name:_______ NetID:_______
Identify the best response from the answers for each question/subquestion.
Write down your choice clearly for each question/subquestion.
There are 26 questions each carries 4 points, question 26 is the bonus question.
1. If a set of data is normally distributed, about what percent of data will be
between 2 standard deviations from the mean.
(a) 68%
(b) 75%
(c) 95%
(d) 90%
2. If a set of data is normally distributed with mean 80 and standard
deviation 7, using 68-95-99.7 rule about 95% data will fall within what
two values?
(a) (73, 87) (b) (60,100) (c) (66,94) (d) (68,95)
3. Let z be a random variable with a standard normal distribution. Find the
probability P(–1.7  z  –0.8.
(a) .955
(b) .167
(c) .212
(d) .788
4-5. A certain company makes 12-volt car batteries. After many years of product testing, the
company knows that the average life of a battery is normally distributed, with a mean of 44
months and a standard deviation of 8 months.
4. If the company guarantees a full refund on any battery that fails within
the 36-month period after purchase, what percentage of its batteries will
the company expect to replace?
(a) .8413
(b) .1094
(c) .1587
(d) .2177
5. If the company does not want to make refunds for more than 10% of its
batteries under the full-refund guarantee policy, for how long should the
company guarantee the batteries (to the nearest month)?
(a) 35 months
(b) 52 months
(c) 34 months
(d) 33 months
6-8. The average weight in a large population of bears is 1,000 lbs. The population
standard deviation is 100 lbs. Suppose that a simple random sample of 64 bears is
selected from this population. Let x denote the sample average and take it to be
normally distributed.
6. The mean of the sampling distribution of x is
(a) 1,000 lbs (b) 150 lbs
(c) 275 lbs
(d) 125 lbs
7. The standard deviation of the sampling distribution of x is
(a) 10 lbs
(b) 100 lbs
(c) 8 lbs
(d) 12.5 lbs
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8. Determine the probability that x falls within 5 lbs of the population mean.
(a) .0500
(b) .6892
(c) .3108
(d) .4031
9-11. In 2004, ACT, Inc. reported that 468 of 600 randomly selected college freshmen
returned to college the next year. Estimate the national freshmen-to-sophomore retention
rate p.
9. The point estimate for p is.
(a) .78
(b) 468
(c) .20
(d) .72
10. The 90% margin of error in the estimate 𝑝̂ is
(a) .039
(b) .045
(c) .103
(d) .028
11. What is the 90% confidence interval estimate of the percentage of all national
freshmen who return to college the next year?
(a) (0.752, 0.808) (b) (0.769, 0.825) (c) (0.748,0.814) (d) (0.738, 0.784)
12. In preparing a report on the economy, we need to estimate the percentage of
businesses that expect to hire additional employees in the next 60 days. How many
randomly selected businesses do we need to contact to create a 98% confidence
interval with a margin of error of 4%?
(a) 480
(b) 849
(c) 994
(d) 335
13. The sample size needed to estimate a population mean within 16 units with a 95%
confidence when the population standard deviation equals 75 is
(a) 61
(b) 85
(c) 76
(d) 55
14-15. Answer these questions about z- confidence interval or Normal confidence interval, tconfidence interval.
14. What is the t-critical value for 99% confidence interval if the sample size is 5?
(a) 4.032
(b) 3.365
(c) 3.747
(d) 4.604
15. What is the z-critical value for 95% confidence interval if the sample size is 5?
(a) 1.645
(b) 1.96
(c) 2.325
(d) 4.604
16-17. A professor of statistics refutes the claim that the average student spends 5 hours
studying for the midterm exam. She thinks they spend more time than that. A random
sample of 10 students showed a sample mean of 6 hours. The number of hours is
normally distributed with a population standard deviation σ=1.5 hours, calculated value
of test statistic?
16. Which hypotheses are used to test the claim?
(a) 𝐻0 : μ ≠ 5 vs. 𝐻1 : μ = 5
(b) 𝐻0 : μ = 5 vs. 𝐻1 : μ > 5
(c) 𝐻0 : μ ≠ 6 vs. 𝐻1 : μ = 6
(d) 𝐻0 : 𝑥̅ = 6 vs. 𝐻1 : 𝑥̅ > 6
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17. The professor also wants to construct a 90% confidence interval for the
average studying time. Based on the sample information, the 90% confidence
interval is given by,
(a) 6-1.645*1.5/√10, 6+1.645*1.5/√10
(b) 6-1.96*1.5/√10, 6+1.96*1.5/√10
(c) 6-1.833*1.5/√10, 6+1.833*1.5/√10
(d) 5-1.645*1.5/√10, 5+1.645*1.5/√10
18. The mean area μ of the several thousand apartments in a new development by a
certain builder is advertised to be 1250 square feet. A tenant group thinks this is
inaccurate, and suspects that the average is actually less than 1250 square feet.
Apartments are randomly selected and carefully measured. The appropriate
hypotheses to test are
(a) 𝐻0 : μ = 1250 v. 𝐻1 : μ > 1250
(b) 𝐻0 : μ = 1250 v. 𝐻1 : μ < 1250
(c) 𝐻0 : μ = 1250 v. 𝐻1 : μ ≠ 1250
(d) 𝐻0 : μ > 1250 v. 𝐻1 : μ = 1250
19-22. In a random sample of 518 judges, it was found that 276 were introverts. Let p represent
the proportion of all judges who are introverts.
19. Find a point estimate for p.
(a) 0.5638
(b) 0.5432
(c) 0.5328
(d) 0.4672
20. Find a 99% confidence interval for p.
(a) (0.48, 0.59) (b) (0.4687, 0.5787) (c) (0.5328, 0.6628) (d) (0.51, 0.62)
21. Give a brief interpretation of the meaning of the confidence interval you
have found.
(a) We are 1% confident that the true proportion of judges who are introverts
falls above this interval.
(b) We are 99% confident that the true proportion of judges who are introverts
falls within this interval.
(c) We are 99% confident that the true proportion of judges who are introverts
falls outside this interval.
(d) We are 1% confident that the true proportion of judges who are introverts
falls within this interval.
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22. Do you think the conditions np > 5 and nq > 5 are satisfied in this problem?
Explain why this would be an important consideration.
(a) Yes, the conditions are satisfied. This is important because it allows us to
say that is approximately normal.
(b) Yes, the conditions are satisfied. This is important because it allows us to
say that is approximately binomial.
(c) No, the conditions are not satisfied. This is important because it allows us
to say that is approximately binomial.
(d) No, the conditions are not satisfied. This is important because it allows us
to say that is approximately normal.
23-26. When reading a report, you encounter this sentence “The mean salary for high
school teachers in public schools in Michigan is between $48,000 and $52,000 with 95%
confidence.” Assume that the z-confidence interval was used based on a simple random
sample of n = 100 teachers, all of who responded accurately.
[Hint: Use x  E  48000, x  E  52000 , to answer 23, 24.]
23. Sample mean salary for these 100 teachers is
(a) $51,000 (b) $48000
(c) $50,000
(d) none of above
24. What is the margin of error for this confidence interval?
(a) $50,000
(b) $4000
(c) $1000
(d) $2000
25. If the confidence interval is constructed based on sample standard deviation s,
then we will use
(a) confidence interval with normal critical value
(b) confidence interval with t critical value
26. (Bonus Question) To reduce the length of the confidence interval, we will
(a) increase the sample size
(b) decrease the sample size
(c) use a sample with different 100 teachers
(d) none of above
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