Midterm 2 Practice Exam 1 - Confidence Intervals and Hypothesis Testing môn Xác suất thống kê| Trường Đại học Ngoại Thương

21:04, 27/01/2026
Midterm 2 Practice Exam 1 - Confidence Intervals and Hypothesis Testing - Studocu Practice Exam 2A
The following 5 questions are based on this information. Suppose a random sample of 18 Uber
drivers was taken, and the average age X¯ of these drivers was found to be 27.5 years.
Construct a 99% confidence interval for the mean age (µ) of all drivers. Assume that the age of
drivers is normally distributed with a population standard deviation (σ) of 2.3 years.
1. The standard error (SE) of X¯ is Select one: a. 0.54 b. 0.13 c. 2.3 d. 6.48
2. The critical value (CV) used for a 99% interval estimate is Select one: a. 0.01 b. 2.32 c. 2.58 d. 0.005
3. The 99% confidence interval estimate of µ is Select one: a. 27.5 ± 2.3 b. 27.5 ± 0.54 c. 27.5 ± 1.26 d. 27.5 ± 1.39
4. The company claims that average age of drivers is 26.9 years. In light of the sample
evidence and at the 1% level of significance, Select one:
a. Your claim is statistically justified
b. Your claim is not statistically justified
5. If we decrease the confidence level (1-α) from 0.99 to 0.95, the margin of error (ME) of
the confidence interval estimate will Select one: a. be zero b. decrease c. increase d. stays the same
The following 6 questions are based on this information. A large cycle company reported that in
2010, 65% of parents of children (between the ages of 8 to 12), bought their children a cycle.
That same company has stated that cycle purchases for that same age group have gone up. They
surveyed 300 parents of children and found that 230 of them have bought cycle to their children. 21:04, 27/01/2026
Midterm 2 Practice Exam 1 - Confidence Intervals and Hypothesis Testing - Studocu
6. Specify the null and alternative hypotheses. Select one:
a. H(0): p≥0.65 Versus H(a): p<0.65
b. H(0): p≤0.65 Versus H(a): p>0.65
7. The standard error (SE) of p¯ is Select one: a. 0.024 b. 0.037 c. 0.058 d. 0.047
The following 5 questions are based on this information. In 2017, it was reported that women
sent on average 3,000texts per month. It is believed that the number of texts sent has increased.
In fact, a recent random sample of 60 women showed that they send an average 3,500 texts per
month(X¯=3,500 texts ) with a sample standard deviation of 600 texts (s=600 texts ). Assume
that the random variable, number of texts sent by women(denoted by X), is normally distributed.
Is this sufficient statistical evidence to show that women are now sending on average more than 3000 texts per month?
8. Specify the null and alternative hypotheses. Select one:
a. H(0): μ≥3,000 versus H(a): μ<3,000
b. H(0): μ≤3,000 versus H(a): μ>3,000
9. The standard error (SE) of X¯ is Select one: a. 3.01 b. 0.24 c. 77.45 d. 0.76
10. The test statistics value is Select one: a. 0.66 b. 2.08 c. 0.53 d. 6.45 11. The p-value is Select one: a. 0.301 b. 0.999 c. 0.973 21:04, 27/01/2026
Midterm 2 Practice Exam 1 - Confidence Intervals and Hypothesis Testing - Studocu d. 0.000
12. At α=0.01 and using the p-value Select one:
a. We reject H(0) in favor of H(a)
b. We do not reject H(0)
The following 5 questions are based on this information. Historically, the average number of
boats owned by the people living in the coasts in a lifetime has been 12. An economist believes
that the number is now lower because of recent economic downturns. A recent survey of 30
senior citizens indicates that the average number of boats owned over their lifetime is 10.
Assume that the random variable, number of boats owned in a lifetime (denoted by X), is
normally distributed with a standard deviation (σ ) is 4.5.
13. Specify the null and alternative hypotheses. Select one:
a. H(0): μ≥12 versus H(a): μ<12
b. H(0): μ≤12 versus H(a): μ>12
14. The standard error (SE) of X¯ is Select one: a. 2.5 b. 0.82 c. 10.5 d. 4.5 15. The p-value is Select one: a. 0.03 b. 0.99 c. 0.05 d. 0.00
16. The test statistics value is Select one: a. 0.9 b. -2.43 c. 2.5 d. -2.5
17. At α=0.10 and using the p-value Select one: a. We do not reject H(0) 21:04, 27/01/2026
Midterm 2 Practice Exam 1 - Confidence Intervals and Hypothesis Testing - Studocu
b. We reject H(0) in favor of H(a)
The following 5 questions are based on this information. In a poll of 500 Graduat students, .75%
(p¯=0.75 ) said that they used only Internet for the project and assignment purposes.. The goal is
to construct a 99% confidence interval for the percentage (p ) of Graduatel students who use the
Internet for project and assignment purposes.
18. The standard error (SE) of p¯ is Select one: a. 0.016 b. 0.0004 c. 0.0002 d. 0.019
19. The critical value (CV) needed for 99% confidence interval estimation is Select one: a. 1.28 b. 1.64 c. 1.96 d. 2.58
20. The 99% confidence interval estimate of p is Select one: a. 0.75 ± 0.05 b. 0.44 ± 0.03 c. 0.44 ± 0.002 d. 0.75 ± 0.15
21. Suppose around the period the above poll was conducted, The Dean of a university made
a personal statement saying that .85% of Graduate students used only the Internet for
assignment purposes In light of the sample evidence and at the 1% level of significance, Select one:
a. We can reject the Dean's claim
b. We cannot reject the Dean's claim
22. A Dean of the university wishes to collect new random sample with the aim of building a
new confidence interval at the 99% confidence level for p . Using the current sample
proportion (from the 500 graduate students poll ) as a basis, what sample size (n) would
the journalist require to achieve a 10% margin of error? Select one: a. 250 b. 73 c. 125 21:04, 27/01/2026
Midterm 2 Practice Exam 1 - Confidence Intervals and Hypothesis Testing - Studocu d. 500
The following 5 questions are based on this information. A survey indicates that the proportion
of girls in the total youth in the United States is 51% (p=0.51 ). We will take a random sample of 400 U.S. youths.
23. The sampling distribution of p¯ , the sample proportion of U.S. youths who are girls, is: Select one:
a. is normal because np≥5 and n(1−p)≥5
b. is not normal because the sample size is too small
c. is not normal because n < 500
d. is normal because the only requirement is for n to be greater than 30 and that is met
24. The standard error (SE) of p¯ is Select one: a. 0.006 b. 0.038 c. 0.001 d. 0.025
25. What is the probability that a random sample of 400 U.S. youth will provide a sample
proportion (p¯ ) that is within 0.03 of the population proportion (p )? Select one: a. 23% b. 43% c. 76.99% d. 57%
26. What is the probability (rounded) that a random sample of 400 U.S youth will provide a
sample proportion (p¯ ) that is within 0.07 of the population proportion (p )? Select one: a. 1% b. 89% c. 2% d. 99%
27. Say, you took a random sample of 400 U.S. youth, and found out that the sample
proportion (p¯ ) for this sample to be 0.42. Select one:
a. This is NOT a rare finding because the likelihood of p ¯ =0.42 is quite large as we saw in the previous question
b. This is a rare finding because the likelihood of p ¯ =0.42 is quite small as we saw
in the previous question 21:04, 27/01/2026
Midterm 2 Practice Exam 1 - Confidence Intervals and Hypothesis Testing - Studocu
The following 6 questions are based on this information. According to a journalist of BBC News
from April 2016, the average price of milk at all U.S. supermarkets was $3.00 (µ). The
population standard deviation (σ) of milk prices is $1.75. Let X be a random variable denoting
milk price at super market. We plan to take a random sample of 36 supermarkets.
28. What is the sampling distribution of X¯ when sample of size 36 is used? Select one:
a. Is not normal because the sample size is too small
b. Is normal due to the Central Limit Theorem
c. Is normal due to the Chebyshev’s Theorem
d. Is not normal because the sample size is too large
29. Suppose that we reduce the sample size from 36 to 16. The sampling distribution of X¯ will be normal only if Select one:
a. X has a bi-modal distribution
b. X has a normal distribution
c. X has a uniform distribution d. X has a skewed distribution
30. What is the probability that a random sample of 36 supermarkets will provide an average
milk price (X¯ ) that is more than $3.50? Select one: a. 31% b. 9% c. 4.5% d. 45.5%
31. What is the probability that a random sample of 36 supermarkets will provide an average
milk price (X¯ ) that is within $0.50 of the population mean (μ )? Select one: a. 9% b. 91% c. 38% d. 62%
32. The probability in the PREVIOUS question would _________if we were to increase the sample size to 72. Select one: a. be zero b. increase c. stay the same d. decrease 21:04, 27/01/2026
Midterm 2 Practice Exam 1 - Confidence Intervals and Hypothesis Testing - Studocu
Use this information to answer the following 6 questions::
The U.S. Police department wants to know if a new campaign, to make citizens aware of the
dangers of drunk driving, has been effective. They count the number of drivers who have been
stopped with more alcohol in their body than the law permits for each day of the week in the
week before and the week a month after the campaign starts. The results are in this data link: Da y of Aft Befo We er re ek M 1 6 T 8 3 W 6 8 Th 2 9 F 0 6 S 2 15 Su 7 9
Assume that the number of stops of drunk drivers (before as well as after the campaign) is each
normally distributed. Use the following notation:
μ(d): The mean of the difference in number of daily stops of drunk drivers between those
days after and those days before the campaign.
33. Specify the null and alternative hypotheses using correct notations. Select one:
a. H(0): μ(d)≥0 Versus H(a): μ(d)<0
b. H(0): μ(d) < 0 Versus H(a): μ(d)≥0
34. What is the value of the test statistic? Select one: a. -2.05 b. 1.44 c. 1.67 d. -1.44
35. At alpha= 0.05, What is the critical value of the test? Select one: a. -1.94 b. -1.44 21:04, 27/01/2026
Midterm 2 Practice Exam 1 - Confidence Intervals and Hypothesis Testing - Studocu c. 1.44 d. 1.94
36. At α=0.05 and using the correct critical value from the preceding question Select one: a. We do not reject H(0)
b. We reject H(0) in favor of H(a) 37. What is the p-value? Select one: a. 0.01 b. 0.05 c. 0.043076 d. 0.14529072
Use this information to answer the following 6 questions:
A study is being conducted to compare the average medical training time for two groups of
doctors: those who work for the government and those employed by private hospitals. From a
random sample of 22 government-employed doctors, average training time was 62 hours, with a
sample standard deviation of 10 hours. In a random sample of 16 doctors working in hospitals,
training time was 65.4 hours, with a sample standard deviation of 12.3 hours. Assume that
training time for each group is normally distributed. Use the following notations:
μ1: The mean training time for the population of doctors employed by the government.
μ2: The mean training time for the population of doctors by private hospitals.
The goal of the statistical analysis is to determine whether the sample data support the hypothesis
that average training time for government-employed doctors is higher than those employed by private hospitals.
38. What is the null hypothesis H(0)? Select one: a. μ1- μ2 ≥ 0 b. μ1- μ2 < 0 c. μ1- μ2 = 0
d. μ1- μ2 ≤ 0
39. What is the alternative hypothesis H(a)? Select one: a. μ1- μ2 ≤ 0 b. μ1- μ2 ≥ 0 21:04, 27/01/2026
Midterm 2 Practice Exam 1 - Confidence Intervals and Hypothesis Testing - Studocu c. μ1- μ2 > 0 d. μ1- μ2 = 0
40. What is the standard error of X¯1−X¯2? Select one: a. 10.15 b. 3.74 c. 5.29 d. 2.83
41. What is the value of the test statistic? Select one: a. 0.65 b. 1.35 c. -0.9 d. 1.22 42. What is the p-value? Select one: a. 0.12 b. 0.01 c. 0.81 d. 0.99 21:04, 27/01/2026
Midterm 2 Practice Exam 1 - Confidence Intervals and Hypothesis Testing - Studocu