# Statistics

```A sample space consists of 46 separate events that are equally likely. What is
the probability of each? 1/46
If you flip a coin three times, the possible outcomes are HHH, HHT, HTH,
HTT, THH, THT, TTH, TTT. What is the probability of getting at least one head? 7/8
A die with 12 sides is rolled. What is the probability of rolling a number less than 11? Is this the same
as rolling a total less than 11 with two six-sided dice? Explain. 5/6
A committee of three people is to be formed. The three people will be selected from a list of five
possible committee members. A simple random sample of three people is taken, without
replacement, from the group of five people. Using the letters A, B, C, D, E to represent the five
people, list the possible samples of size three and use your list to determine the probability that B is
included in the sample. (Hint: There are 10 possible samples.) 0.6
Based on meteorological records, the probability that it will snow in a certain town on January 1st is
0.413. Find the probability that in a given year it will not snow on January 1st in that town.
0.587
The probability that Luis will pass his statistics test is 0.94. Find the probability that he will fail his
statistics test. 0.06
In the first series of rolls of a die, the number of odd numbers exceeded the number of even
numbers by 5. In the second series of rolls of the same die, the number of odd numbers exceeded
the number of even numbers by 11. Determine which series is closer to the 50/50 ratio of odd/even
expected of a fairly rolled die.
The series closer to the theoretical 50/50 cannot be determined unless the total number of rolls for
both series is given.
In a poll, respondents were asked whether they had ever been in a car accident. 220 respondents
indicated that they had been in a car accident and 370 respondents said that they had not been in a
car accident. If one of these respondents is randomly selected, what is the probability of getting
someone who has been in a car accident? Round to the nearest thousandth.
0.373
The data set represents the income levels of the members of a country club. Estimate the
probability that a randomly selected member earns at least \$98,000.
112,000 126,000 90,000 133,000 94,000 112,000 98,000 82,000 147,000 182,000 86,000
105,000
140,000 94,000 126,000 119,000 98,000 154,000 78,000 119,000
0.7
The distribution of B.A. degrees conferred by a local college is listed below, by major.
MajorFrequency
English 2073
Mathematics 2164
Chemistry 318
Physics 856
Liberal Arts 1358
Engineering 868
9313
What is the probability that a randomly selected degree is not in Business?
0.8200
Suppose you have an extremely unfair die: The probability of a 6 is 3/8, and the probability of each
other number is 1/8. If you toss the die 32 times, how many twos do you expect to see?
4
Suppose you have an extremely unfair coin: the probability of a head is 1/3 and the probability of a
tail is 2/3. If you toss the coin 72 times, how many heads do you expect to see?
24
A study of two types of weed killers was done on two identical weed plots. One weed killer killed
15% more weeds than the other. This difference was significant at the 0.05 level. What does this
mean?
The probability that one weed killer performed better by chance alone is less than 0.05 .
Suppose you buy 1 ticket for \$1 out of a lottery of 1000 tickets where the prize for the one winning
ticket is to be \$500. What is your expected value?
-\$0.50
A class consists of 50 women and 82 men. If a student is randomly
selected, what is the probability that the student is a woman?
50/132
A study of students taking Statistics 101 was done. Four hundred students who studied for more than
10 hours averaged a B. Two hundred students who studied for less than 10 hours averaged a C. This
difference was significant at the 0.01 level. What does this mean?
There is less than a 0.01 chance that the first group's grades were better by chance alone.
A population proportion is to be estimated. Estimate the minimum sample size needed to achieve a
margin of error E = 0.01with a 95% degree of confidence.
10,000
Suggest the cause of the correlation among the data.
The graph shows strength of coffee (y) and number of scoops used to make 10 cups of coffee
(x). Identify the probable cause of the correlation.
The variation in the x variable is a direct cause of the variation in
the y variable.
Eleven female college students are selected at random and asked their heights. The heights
(in inches) are as follows:
67, 59, 64, 69, 65, 65, 66, 64, 62, 64, 62
Estimate the mean height of all female students at this college. Round your answer to the
nearest tenth of an inch if necessary.
64.3 inches
Among a random sample of 150 employees of a particular company, the mean commute
distance is 29.6 miles. This mean lies 1.2 standard deviations above the mean of the
sampling distribution. If a second sample of 150 employees is selected, what is the
probability that for the second sample, the mean commute distance will be less than 29.6
miles?
0.8849
Sample size = 400, sample mean = 44, sample standard deviation = 16. What is the margin of
error?
1.6
Which line of the three shown in the scatter diagram below fits the data best?
C
Of the 6796 students in one school district, 1537 cannot read up to grade level. Among a
sample of 812 of the students from this school district, 211 cannot read up to grade level.
Find the sample proportion of students who cannot read up to grade level.
0.26
A researcher wishes to estimate the proportion of college students who cheat on exams. A
poll of 490 college students showed that 33% of them had, or intended to, cheat on
examinations. Find the margin of error for the 95% confidence interval.
0.0425
Select the best estimate of the correlation coefficient for the data depicted in the scatter
diagram.
-0.9
Select the best estimate of the correlation coefficient for the data depicted in the scatter
diagram.
0.9
A psychologist claims that more than 29 percent of the professional
population suffers from problems due to extreme shyness. Assuming that a
hypothesis test of the claim has been conducted and that the conclusion is
failure to reject the null hypothesis, state the conclusion in non-technical
terms.
There is not sufficient evidence to support the claim that the true proportion
is greater than 29 percent.
z = 1.8 for Ha: µ > claimed value. What is the P-value for the test?
0.0359
A manufacturer claims that the mean amount of juice in its 16 ounce bottles is 16.1 ounces.
A consumer advocacy group wants to perform a hypothesis test to determine whether the
mean amount is actually less than this. The mean volume of juice for a random sample of 70
bottles was 15.94 ounces. Do the data provide sufficient evidence to conclude that the mean
amount of juice for all 16-ounce bottles, µ, is less than 16.1 ounces? Perform the appropriate
hypothesis test using a significance level of 0.10. Assume that = 0.9 ounces.
The z of -1.49 provides sufficient evidence to conclude that the mean amount of
juice is less than 16.1 oz.
At one school, the mean amount of time that tenth-graders spend watching television each
week is 18.4 hours. The principal introduces a campaign to encourage the students to watch
less television. One year later, the principal wants to perform a hypothesis test to determine
whether the average amount of time spent watching television per week has decreased.
Formulate the null and alternative hypotheses for the study described.
Ho: µ = 18.4 hours H a: µ < 18.4 hours
A two-tailed test is conducted at the 5% significance level. What is the left tail percentile
required to reject the null hypothesis?
97.5%
A study of a brand of "in the shell peanuts" gives the following results:
A significant event at the 0.01 level is a fan getting a bag with how many peanuts?
25, 30 or 55 peanuts
A consumer advocacy group claims that the mean amount of juice in a 16
ounce bottled drink is not 16 ounces, as stated by the bottler.
Determine the null and alternative hypotheses for the test described.
H0: µ = 16 ounces Ha: µ ¹ 16 ounces
In the past, the mean running time for a certain type of flashlight battery has been 9.8 hours.
The manufacturer has introduced a change in the production method and wants to perform
a hypothesis test to determine whether the mean running time has increased as a result. The
hypotheses are:
H0 : µ = 9.8 hours
Ha : µ > 9.8 hours
Suppose that the results of the sampling lead to rejection of the null hypothesis. Classify that
conclusion as a Type I error, a Type II error, or a correct decision, if in fact the mean running
time has not increased.
Type I error
In 1990, the average duration of long-distance telephone calls originating in one town was
9.3 minutes. A long-distance telephone company wants to perform a hypothesis test to
determine whether the average duration of long-distance phone calls has changed from the
1990 mean of 9.3 minutes. Formulate the null and alternative hypotheses for the study
described.
Ho: µ = 9.3 minutes Ha: µ ¹ 9.3 minutes
without computing a P-value, determine whether the alternate hypothesis is supported and
give a reason for your conclusion.
Ha is not supported; x̄ is less than 1 standard deviation above the claimed mean.
A golfer wished to find a ball that would travel more than 170 yards when hit with his 6-iron
with a club head speed of 90 miles per hour. He had a golf equipment lab test a low
compression ball by having a robot swing his club 12 times at the required speed. State the
null and alternative hypotheses for this test.
A golfer wished to find a ball that would travel more than 160 yards when hit with his 7 -iron
with a club speed of 90 miles per hour. He had a golf equipment lab test a low compression
ball by having a robot swing his club 8 times at the required speed.
H0: µ < 170; Ha: µ = 170
Data from this test resulted in a sample mean of 163.2 yards with a sample standard
deviation of 5.8 yards. Assuming normality, carry out a hypothesis test at the 0.05
significance level to determine whether the ball meets the golfer's requirements. Use the
partial t-table below to solve this problem.
Do not reject the null hypothesis. The data do not provide sufficient
evidence that the average distance is greater than 160 yards.
Which of the following statements is true?
The t distribution cannot be used when finding a confidence interval for the population
mean with a small sample whenever the sample comes from a symmetric population.
A 95% confidence interval for the mean of a normal population is found to be 15.6 < µ <
25.2. What is the margin of error?
4.8
The margin of error in estimating the population mean of a normal population is E = 9.3
when the sample size is 15. If the sample size had been 18 and the sample standard
deviation did not change, would the margin of error be larger or smaller than 9.3? Explain
Smaller. E decreases as the square root of the sample size gets larger.
One hundred people are selected at random and tested for colorblindness to determine
whether gender and colorblindness are independent. The following counts were observed.
Colorblind
Not
Total
Colorblind
Male
Female
Total
8
2
10
52
38
90
60
40
100
State the null and alternative hypothesis for the test associated with this data.
H0: Colorblindness and gender are independent characteristics.
Ha: Colorblindness and gender are related in some way.
One hundred people are selected at random and tested for colorblindness to determine
whether gender and colorblindness are independent.
The critical value of X 2 for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of
the X2 statistic is 4.613, state your conclusion about the relationship between gender and
colorblindness.
Reject H0. There is sufficient evidence to support the claim that gender and colorblindness
are related.
Lesson 3 Exam
Question 1
5 / 5 points
The normal monthly precipitation (in inches) for August is listed for 20 different U.S. cities.
Find the median of the data.
3.45 in.
Question 2
5 / 5 points
The mathematics SAT scores of the seven students in a mathematics seminar are 533, 553,
578, 586, 619, 626, and 633. Suppose that the student with the score 533 drops the seminar
and is replaced by a student with a score of 765. What will happen to the mean and the
median scores of the class?
Both the median and the mean will increase.
Question 3
5 / 5 points
The number of vehicles passing through a pharmacy drive-up line with two windows during
each 15-minute period was recorded. The results are shown below. Find the median number
of vehicles going through the line in a fifteen-minute period.
16 8 24 22 30 19 18 27 11 15
17 24 26 23 7 25 21 16 20 14
19.5
Question 4
0 / 5 points
The federal government requires a car manufacturer to have a minimum miles per gallon
(mpg) average over the cars it makes. Suppose that the models and mpg's for a
manufacturer are Corsair (31 mpg), Futura (30 mpg), Retro (37 mpg), and Envy (44 mpg).
Twenty percent of the cars sold are Corsairs, 30% are Futuras, 40% are Retros, and 10% are
Envys. Find the average mpg for this manufacturer.
Question options:
35.5 mpg
34.0 mpg
34.4 mpg
None of the above
Question 5
5 / 5 points
Suppose that your income is at the 81st percentile of wage earners in the United States.
What percent of wage earners make more than you do?
19%
Question 6
5 / 5 points
The grocery expenses for six families were \$80.86, \$47.74, \$57.92, \$81.08, \$75.18, and
\$88.08. Compute the mean grocery bill. Round your answer to the nearest cent.
\$71.81
Question 7
5 / 5 points
Find the mode(s) for the given sample data. 20, 49, 46, 43, 49, 43, 49, 20, 22
49
Question 8
0 / 5 points
A softball player has a batting average of exactly .300 and no more than
60 times at bat. Suppose this player gets 5 hits in her next 6 times at
bat. What is the highest possible average she could now have?
Question options:
.500
.833
.348
There is insufficient information to answer the question
Question 9
5 / 5 points
The weights (in ounces) of 21 cookies are shown. Find the median weight.
0.62 1.25 0.60 1.62 0.75 0.74 1.35
1.25 1.53 0.99 0.62 1.25 1.28 0.66
0.47 1.25 0.74 1.28 1.72 0.75 0.56
Question options:
0.99 ounces
Question 10
5 / 5 points
The following data set is the GPAs of the students in a statistics class.
1.93, 1.99, 2.00, 2.04, 2.12, 2.34, 2.55, 2.55, 2.75, 2.75,
2.80, 2.80, 2.85, 3.02, 3.12, 3.22, 3.31, 3.33, 3.45, 3.69
What percentile is a GPA of 2.34?
Question options:
Question 11
0 / 5 points
The batting averages of the first three batters in the Eureka College women's softball team
lineup are .310, .301, and .277. If the first three batters are considered as the "lead -off
group", what is the batting average of the group?
Question options:
.301
.296
There is insufficient information to answer the question
None of the above
Question 12
5 / 5 points
Use the range rule of thumb to approximate the standard deviation.
22,29, 21, 24, 27, 28, 25, 38
4.25
Question 13
5 / 5 points
Find the standard deviation for the given data. Round your answer to one more decimal
place than the original data.
15, 42, 53, 7, 9, 12, 14, 28, 47
Question options:
17.8
Question 14
5 / 5 points
Find the mode(s) for the given sample data. 7.29, 7.41, 7.56, 7.29, 7.88, 7.99, 7.62
7.29
Question 15
5 / 5 points
Suppose that there are 400 students in your school class. What class rank is the 20th
percentile?
80
Question 16
0 / 5 points
The host of a dinner party purchases wine based on the weighted average of clarity (10%),
bouquet (5%), friendliness to the palate (5%), storage ability of opened bottles (40%), and
price (40%). Suppose that Bone Ranch Wave has scores in these categories of 4, 5, 3, 8, and
9, respectively. What is its rating?
Question options:
5.80
5.00
7.60
None of the previous
Question 17
5 / 5 points
Use the range rule of thumb to approximate the standard deviation.
496,598, 503, 528, 565, 601, 576, 543
26.25
Question 18
5 / 5 points
Find the standard deviation for the given data. Round your answer to one more decimal
place than the original data.
22, 29, 21, 24, 27, 28, 25, 36
4.8
Question 19
5 / 5 points
Consider the distribution of heights of all the players in the National Basketball Association.
What would you expect the shape of the distribution to be?
Skewed left
Question 20
5 / 5 points
Al and Joe are two county sheriff's deputies assigned to watch for traffic violations. Their
arrest and conviction records for May and June are shown below.
Who had the best conviction percentage in May?
Joe
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