Download Statistics 300 - THS Mathematics Department

Advanced College Prep Statistics
Final Review
2014-2015
Name: ________________________
Choose the best answer
1) High temperatures in a certain city for the month of August follow a uniform
distribution over the interval 61ºF to 91ºF. Find the high temperature which 90% of the
August days exceed.
a. 71ºF
b. 64ºF
c. 88ºF
d. 91ºF
2) Find the area under the standard normal curve to the right of z = 1.
a. 0.8413
b. 0.1587
c. 0.5398
d. 0.1397
3) For a standard normal curve, find the z-score that separates the bottom 30% from the
top 70%.
a. -0.1249
b. -0.4711
c. -0.5244
d. -0.9823
4) IQ test scores are normally distributed with a mean of 101 and a standard deviation of
20. An individual’s IQ score is found to be 111. Find the z-score corresponding to this
value.
a. 2.00
b. 0.50
c. -2.00
d. -0.50
5) Suppose that prices of a certain model of new homes are normally distributed with a
mean of $150,000. Find the percentage of buyers who paid between $150,000 and
$152,400 if the standard deviation is $1200. (Empirical Rule!)
a. 34%
b. 47.5%
c. 99.7%
d. 68%
6) A physical fitness association is including the mile run in its secondary-school fitness
test. The time for this event for boys in secondary school is known to possess a normal
distribution with a mean of 450 seconds and a standard deviation of 50 seconds. Between
what times do we expect most (approximately 95%) of the boys to run the mile?
a. between 355 and 545 seconds
b. between 352 and 548 seconds
c. between 0 and 532.28 seconds
d. between 367.75 and 532.28 seconds
7) The number of violent crimes committed in a day possesses a distribution with a mean
of 4.1 crimes per day and a standard deviation of 6 crimes per day. A random sample of
100 days was observed, and the sample mean number of crimes for the sample was
calculated. Describe the sampling distribution of the sample mean.
a. shape unknown with mean = 4.1 and standard deviation = 0.6
b. approximately normal with mean = 4.1 and standard deviation = 6
c. approximately normal with mean = 4.1 and standard deviation = 0.6
d. shape unknown with mean = 4.1 and standard deviation = 6
8) The average score of all golfers for a particular course has a mean of 79 and a standard
deviation of 3.5. Suppose 49 golfers played the course today. Find the probability that the
average score of the 49 golfers exceeded 80.
a. .1293
b. .4772
c. .3707
d. .0228
9) The grade point averages for 10 randomly selected students in a statistics class with
125 students are listed below. Find the best point estimate for the mean.
2.4
2.5
1.9
3.5
2.1
3.1
2.9
3.9
3.6
2.6
a. 3.17
b. 2.6
c. 2.85
d. 28.5
10) Suppose a 95% confidence interval for  turns out to be (120, 310). To make more
useful inferences from the data, it is desired to reduce the width of the confidence interval.
Which of the following will result in a reduced interval width?
a. Decrease the confidence level
b. Increase the sample size
c. Increase the standard deviation
d. All of the choices will result in a reduced interval width
11) Suppose a 90% confidence interval for  turns out to be (110, 260). Based on the
interval, do you believe the average is equal to 270?
a. Yes, and I am 100% sure of it.
c. Yes, and I am 90% sure of it.
b. No, and I am 100% sure of it.
d. No, and I am 90% sure of it.
12) A nurse at a local hospital is interested in estimating the birth weight of infants,
which is known to be normally distributed. How large a sample must she select if she
desires to be 90% confident that the true mean is within 4 ounces of the sample mean?
The standard deviation of the birth weights is known to be 6 ounces.
a. 6
b. 3
c. 2
d. 7
13) Find the critical t-value that corresponds to confidence level of 99% and n = 10.
a. 2.281
b. 2.262
c. 3.250
d. 3.169
14) Construct a 95% confidence interval for the population mean  . Assume the
population has a normal distribution. A sample of 20 college students had mean annual
earnings of $3120 with a standard deviation of $677.
a. ($1324, $ 1567)
b. ($2135, $2567)
c. ($2803, $3437)
d. ($2657, $2891)
15) A survey of 100 fatal accidents showed that 43 were alcohol related. Find a point
estimate for p, the population proportion of accidents that were alcohol related.
a. 0.43
b. 0.301
c. 0.754
d. 0.57
16) A university dean is interested in determining the proportion of students who receive
some sort of financial aid. Rather than examine the records for all students, the dean
randomly selects 200 students and finds that 118 of them are receiving financial aid. Use
a 98% confidence interval to estimate the true proportion of students on financial aid.
a. .59  .003
b. .59  .006
c. .59  .081
d. .59  .564
17) A private opinion poll is conducted for a politician to determine what proportion of
the population favors decriminalizing marijuana possession. How large a sample is
needed in order to be 99% confident that the sample proportion will not differ from the
true proportion by more than 5%?
a. 543
b. 1327
c. 666
d. 13
18) Find the critical values, X 12 a / 2 and X a2 / 2 , for c = 0.98 and n = 20.
a. 10.117 and 32.852 b. 7.633 and 36.191 c. 8.907 and 38.582 d. 6.844 and 36.191
19) Assume that the heights of women are normally distributed. A random sample of 20
women has a mean height of 62.5 inches and a standard deviation of 1.2 inches.
Construct a 98% confidence interval for the population variance  2 .
a. (0.9, 1.9)
b. (0.6, 3.0)
c. (0.8, 3.6)
d. (0.8, 3.8)
20) The mean age of bus drivers in Chicago is greater than 46.1 years. If a hypothesis test
is performed, how should you interpret a decision that rejects the null hypothesis?
a. There is sufficient evidence to reject the claim  > 46.1.
b. There is sufficient evidence to support the claim  > 46.1.
c. There is not sufficient evidence to support the claim  > 46.1.
d. There is not sufficient evidence to reject the claim  > 46.1.
21) Suppose you want to test the claim that   3.5. Given a sample size of n = 39 and
a level of significance of  = 0.05, when should you reject H O ?
a. Reject
b. Reject
c. Reject
d. Reject
H O if the test statistic is greater than 1.645 or less than -1.645
H O if the test statistic is greater than 2.575 or less than –2.575
H O if the test statistic is greater than 1.96 or less than -1.96
H O if the test statistic is greater than 2.33 or less than -2.33
22) You wish to test the claim that   22 at a level of significance of  = 0.01 and are
given sample statistics n = 40, x = 23.8, and s= 4.3. Compute the value of the test statistic.
Round your answer to two decimal places.
a. 2.65
b. 1.96
c. 2.12
d. 3.51
23) Suppose you are using  = 0.01 to test the claim that   26 using a P-value. You are
given the sample statistics n = 40, x = 27.8, and s = 4.3. Find the P-value.
a. 0.0211
b. 0.9942
c. 0.1030
d. 0.0040
24) Find the test statistic t for a sample with n = 15, x = 7.3, s = 0.8, and
 = 0.05 if H O :   7. Round your answer to three decimal places.
a. 1.728
b. 1.631
c. 1.452
d. 1.312
25) A local eat-in pizza restaurant wants to investigate the possibility of starting to
deliver pizzas. The owner of the store has determined that home delivery will be
successful if the average time spent on the deliveries does not exceed 36 minutes. The
owner has randomly selected 21 customers and has delivered pizzas to their home in
order to test if the mean delivery time usually exceeds 36 minutes. Suppose the p-value
for the test was found to be .0277. State the correct conclusion.
a. At  = .03, we fail to reject H O .
c. At  = .02, we reject H O .
b. At  = .05, we fail to reject H O .
d. At  = .025, we fail to reject H O
26) The business college computing center wants to determine the proportion of business
students who have personal computers (PC’s) at home. If the proportion exceeds 25%,
then the lab will scale back a proposed enlargement of its facilities. Suppose 250 business
students were randomly sampled and 85 have PC’s at home. What assumptions are
necessary for this test to be satisfied?
a. The population has an approximately normal distribution.
b. The sample variance equals the population variance.
c. The sample mean equals the population mean.
d. None of the above are necessary.
27) Compute the test statistic, X 2 , to test the claim  2  9.6 if n = 20,
s 2 = 18.6, and  = 0.01.
a. 12.82
b. 36.813
c. 33.41
d. 9.322
Answer each question.
28) The analytic scores on a standardized aptitude test are known to be normally
distributed with mean  =610 and standard deviation  =115.
a. Draw a normal curve with the parameters labeled.
b. Shade the region that represents the proportion of test takers who scored less
than 725.
c. Suppose that the area under the normal curve to the left of X = 725 is 0.8413.
Provide two interpretations of this result.
1. _________________________________________________________
2. ________________________________________________________
29) In a recent study of 96 eighth graders, the mean number of hours per week that they
watched television was 21.6. Assume s = 5.3 hours.
a. Find the 95% confidence interval of the mean.
b. If the standard deviation is doubled to 10.6, what will be the effect on the
confidence interval?
30) In a survey of 10 golfers, 2 were found to be left-handed. Is it practical to construct
the 90% confidence interval for the population proportion, p? Explain.
31) The mean age of bus drivers in Chicago is 56.4 years. Write the null and alternative
hypotheses.
H 0 = _____________________
H A = _______________________
32) The mean age of bus drivers in Chicago is 53.5 years. Identify the Type I and Type II
errors for the hypothesis test of this claim.
Type I:__________________________________________________________________
________________________________________________________________________
Type II: ________________________________________________________________
________________________________________________________________________
33) A group of 49 randomly selected students has a mean age of 22.4 years with a
standard deviation of 3.8. According to a recent survey, the mean age should be  = 21.9
years. Test this hypothesis that the mean is actually higher by constructing a 98%
confidence interval for the population mean.
34) Fifty-five percent of registered voters in a congressional district are registered
Democrats. The Republican candidate takes a poll to assess his chances in a twocandidate race. He polls 1200 potential voters and finds that 621 plan to vote for the
Democratic candidate. Does the Republican candidate have a chance to win? Test the
hypothesis that the proportion is less than 55%. Use  = 0.05.
35) According to a prestigious historical society, in 1999 7.2% of recent high school
graduates believe that the Romans invented mayonnaise. A classics scholar believes that
the percentage has increased since then. He randomly selects 125 recent high school
graduates and finds that 17 of them believe in the Roman invention of mayonnaise. Test
this researcher’s claim at the  = 0.01 level of significance.
36) A fast food outlet claims that the mean waiting time in line is less than 3.6 minutes. A
random sample of 20 customers has a mean of 3.4 minutes with a standard deviation of
0.8 minute. If  = 0.05, test the fast food outlet’s claim using P-values.