Question 1

Solve the problem. Round your answer to one decimal place unless otherwise indicated.
-A researcher for a car insurance company wishes to estimate the mean annual premium that men aged 20-24 pay for their car insurance. When 16 men aged between 20 and 24 were randomly selected and surveyed on their annual car insurance premiums, a mean of $760 was obtained. Based on this sample statistic, what is the best estimate of the mean annual car insurance premium for all men aged between 20 and 24? Round your answer to the nearest dollar.
A)$741
B)$750
C)$760
D)$737

Accepted Answer

The best estimate of the mean annual car insurance premium for all men aged between 20 and 24, based on the sample statistic, is the sample mean itself, which is $760.

Question 2

Solve the problem. Round your answer to one decimal place, if necessary.
-The distribution of sample means for a group of test scores for samples of 100 scores is normal with a mean of 63.9 and a standard deviation of 1.8. Suppose you take a sample of 100 test scores and find that the mean is 65.5.
How many standard deviations is the sample mean from the mean of the distribution of sample means?
A)1.6 standard deviation(s)above the mean
B)0.8 standard deviation(s)above the mean
C)0.9 standard deviation(s)above the mean
D)8.9 standard deviation(s)above the mean

Accepted Answer

C

Question 3

There are 310 teachers at a college. In a sample of 118 teachers from this college,the proportion who had doctorates was 0.55. Based on that sample statistic, what is the best estimate of the proportion for all teachers at
This college?
A)171
B)0.45
C)0.55
D)0.58

Accepted Answer

The best estimate of the proportion for all teachers at the college who have doctorates, based on the sample, is the proportion found in the sample itself, which is 0.55.

Question 4

Nine employees of a company are selected at random and asked how far they commute to work each day. The distances (in miles)are as follows: $$34,16,42,26,22,36,6,47,11$$
Estimate the mean commute distance of all employees of the company.
A)26.7 miles
B)26 miles
C)It is not possible to estimate the population mean from this sample data
D)25.5 miles

Accepted Answer

To estimate the mean commute distance, add all the distances and divide by the number of employees. The calculation is $(34+16+42+26+22+36+6+47+11)/9 = 240/9 = 26.7$ miles.

Question 5

There are 13,259 eligible voters in one town. In a sample of 833 eligible voters from this town, 394 say that they plan to vote in the next mayoral election. Based on this sample statistic, estimate the number of eligible voters in
This town who will vote in the next mayoral election.
A)6146
B)0.47
C)6988
D)6271

Accepted Answer

The proportion of the sample that plans to vote is 394/833. To estimate the number of eligible voters in the town who will vote, multiply this proportion by the total number of eligible voters: (394/833) * 13,259 ≈ 6271.

Question 6

Solve the problem. Round your answer to one decimal place unless otherwise indicated.
-Ten apples of a particular variety are selected at random and weighed. The weights (in ounces)are as follows: $$8.5,7.8,8.1,6.9,7.4,6.1,7,8.6,8.3,7.9$$ Estimate the mean weight of all apples of this variety.
A)7.7 ounces
B)It is not possible to estimate the population mean from this sample data
C)8.0 ounces
D)7.8 ounces

Accepted Answer

The mean weight is calculated by summing all the weights and dividing by the number of apples: (8.5 + 7.8 + 8.1 + 6.9 + 7.4 + 6.1 + 7 + 8.6 + 8.3 + 7.9) / 10 = 7.7 ounces.

Question 7

There are 2140 students in a school district. In a sample of 449 students from this school district, 169 have mathematics scores below grade level. Based on this sample statistic, estimate the number of students in this school district with mathematics scores at or above grade level.
A)1402
B)805
C)280
D)1335

Accepted Answer

The proportion of students below grade level in the sample is 169/449. To estimate the number of students at or above grade level in the entire district, first find the proportion of students at or above grade level in the sample, which is 1 - (169/449). Then, multiply this proportion by the total number of students in the district: (1 - (169/449)) * 2140 ≈ 1335.

Question 8

Solve the problem. Round your answer to one decimal place unless otherwise indicated.
-A sample of nine students is selected from among the students taking a particular exam. The nine students were asked how much time they had spent studying for the exam and the responses (in hours)were as follows:

$$17,7,9,14,11,16,6,19,22$$
Estimate the mean study time of all students taking the exam.
A)13.4 hours
B)12.1 hours
C)It is not possible to estimate the population mean from this sample data
D)14 hours

Accepted Answer

To estimate the mean study time, add all the given times and divide by the number of students: $\frac{17+7+9+14+11+16+6+19+22}{9} = \frac{121}{9} = 13.444...$, which rounds to 13.4 hours.

Question 9

There are 341 teachers at a college. In a sample of 110 teachers from this college, 72 have doctorates. Based on this sample statistic, estimate the number of teachers at this college with doctorates.
A)182
B)223
C)234
D)118

Accepted Answer

The proportion of teachers with doctorates in the sample is 72/110. To estimate the number of teachers with doctorates in the entire college, multiply this proportion by the total number of teachers: (72/110) * 341 ≈ 223.

Question 10

There are 328 teachers at a college. In a sample of 111 teachers from this college, 75 have doctorates. Based on this sample statistic, estimate the number of teachers at this college without doctorates.
A)0.32
B)36
C)106
D)222

Accepted Answer

The answer of There are 328 teachers at a college....

Question 11

Solve the problem. Round your answer to one decimal place, if necessary.
-The distribution of sample means for a group of test scores for samples of 100 scores is normal with a mean of 61.2 and a standard deviation of 1.7. Suppose you take a sample of 100 test scores and find that the mean is 59.3.
How many standard deviations is the sample mean from the mean of the distribution of sample means?
A)1.9 standard deviation(s)below the mean
B)1.1 standard deviation(s)below the mean
C)11.2 standard deviation(s)below the mean
D)1.1 standard deviation(s)above the mean

Accepted Answer

The number of standard deviations the sample mean is from the mean of the distribution of sample means is calculated by the difference between the sample mean and the distribution mean, divided by the standard deviation: (61.2 - 59.3) / 1.7 = 1.9 / 1.7 ≈ 1.1. This indicates the sample mean is 1.1 standard deviations below the mean of the distribution of sample means.

Question 12

There are 13,417 eligible voters in one town. In a sample of 802 eligible voters from this town, 386 say that they plan to vote in the next mayoral election. Based on this sample statistic, estimate the number of eligible voters in this town who will not vote in the next mayoral election.
A)6458
B)0.52
C)416
D)6959

Accepted Answer

The sample shows that 386 out of 802 voters plan to vote, which is approximately 48.13% of the sample. Assuming this percentage applies to the entire population, about 51.87% (100% - 48.13%) of the 13,417 eligible voters might not vote. Therefore, 0.5187 * 13,417 ≈ 6959 eligible voters in the town will not vote in the next mayoral election.

Question 13

Solve the problem. Round your answer to one decimal place unless otherwise indicated.
-When 12 long-distance runners were randomly selected and tested, a mean resting heart rate of 70.0 beats per minute was obtained. Based on this sample statistic, what is the best estimate for the mean resting heart rate for all long-distance runners?
A)66.7 beats per minute
B)68.3 beats per minute
C)71.8 beats per minute
D)70.0 beats per minute

Accepted Answer

The best estimate for the mean resting heart rate for all long-distance runners, based on the sample statistic, is the sample mean itself, which is 70.0 beats per minute.

Question 14

Solve the problem. Round your answer to one decimal place unless otherwise indicated.
-Physiologists often use the forced vital capacity as a way to assess a person's ability to move air in and out of their lungs. A researcher wishes to estimate the forced vital capacity of people suffering from asthma. When 15 asthmatics were randomly selected and tested for their forced vital capacity, a mean forced vital capacity was obtained of 4.4 liters. Based on this sample statistic, what is the best estimate of the mean forced vital capacity
For all asthmatics?
A)4.4 liters
B)4.6 liters
C)4.5 liters
D)4.3 liters

Accepted Answer

The best estimate of the mean forced vital capacity for all asthmatics based on the sample statistic is the sample mean itself, which is 4.4 liters.

Question 15

Eleven female college students are selected at random and asked their heights. The heights (in inches)are as follows: $$68,59,65,71,64,63,68,63,61,65,62$$ Estimate the mean height of all female students at this college.
A)65 inches
B)It is not possible to estimate the population mean from this sample data
C)64.5 inches
D)63.9 inches

Accepted Answer

The answer of Eleven female college students are selected at...

Question 16

There are 2221 students in a school district. In a sample of 452 students from this school district, 161 have mathematics scores below grade level. Based on this sample statistic, estimate the population proportion of students in this district with mathematics scores below grade level.
A)0.36
B)0.07
C)791
D)0.2

Accepted Answer

The proportion of students in the sample with mathematics scores below grade level is calculated by dividing the number of students with scores below grade level (161) by the total number of students in the sample (452), which gives approximately 0.36. This proportion is used to estimate the population proportion.

Question 17

There are 13,427 eligible voters in one town. In a sample of 825 eligible voters from this town, the proportion who say that they plan to vote in the next mayoral election is 0.48 . Based on that sample statistic, what is the best estimate of the proportion for all eligible voters in the town?
A)6380
B)0.47
C)0.52
D)0.48

Accepted Answer

The best estimate of the proportion for all eligible voters in the town is the sample proportion, which is 0.48. This is because the sample proportion is used as an unbiased estimator for the population proportion in statistical analysis.

Question 18

Solve the problem. Round your answer to one decimal place unless otherwise indicated.
-A long-distance phone company wishes to estimate the mean duration of long-distance calls originating in california. A random sample of 15 long-distance calls originating in California yields the following call durations, in minutes.

$$\begin{array} { r r r r r } 
1 & 3 & 2 & 1 & 4 \
23 & 40 & 24 & 16 & 31 \
1 & 19 & 12 & 2 & 37
\end{array}$$
Use the data to obtain an estimate of the mean call duration for all long-distance calls originating in California.
A)14.4 minutes
B)15.2 minutes
C)14.6 minutes
D)14.9 minutes

Accepted Answer

To estimate the mean call duration, add all the call durations together and divide by the number of calls. The total duration is $1 + 3 + 2 + 1 + 4 + 23 + 40 + 24 + 16 + 31 + 1 + 19 + 12 + 2 + 37 = 216$ minutes. Dividing by 15 calls gives a mean duration of $216 / 15 = 14.4$ minutes.

Question 19

In a survey of high school students, 1100 students were randomly selected from California, and the proportion who spoke a second language in addition to English was 0.15. Based on that sample statistic, what is the best
Estimate of the proportion for all high school students in California?
A)165
B)0.85
C)0.5
D)0.15

Accepted Answer

The best estimate of the proportion for all high school students in California who speak a second language, based on the sample statistic, is 0.15. This is because in statistics, the sample proportion is used as the point estimate for the population proportion.

Question 20

There are 2030 students in a school district. In a sample of 483 students from this school district, 164 have mathematics scores below grade level. Based on this sample statistic, estimate the number of students in this school district with mathematics scores below grade level.
A)0.34
B)723
C)689
D)758

Accepted Answer

The proportion of students with scores below grade level in the sample is 164/483. To estimate the number of students with scores below grade level in the entire district, multiply this proportion by the total number of students: (164/483) * 2030 ≈ 689.

Quiz 8: Inferences From Samples to Populations

There are 310 teachers at a college. In a sample of 118 teachers from this college,the proportion who had doctorates was 0.55. Based on that sample statistic, what is the best estimate of the proportion for all teachers at This college?

Nine employees of a company are selected at random and asked how far they commute to work each day. The distances (in miles) are as follows: $34,16,42,26,22,36,6,47,11$ Estimate the mean commute distance of all employees of the company.

There are 13,259 eligible voters in one town. In a sample of 833 eligible voters from this town, 394 say that they plan to vote in the next mayoral election. Based on this sample statistic, estimate the number of eligible voters in This town who will vote in the next mayoral election.

Solve the problem. Round your answer to one decimal place unless otherwise indicated. -Ten apples of a particular variety are selected at random and weighed. The weights (in ounces) are as follows: $8.5,7.8,8.1,6.9,7.4,6.1,7,8.6,8.3,7.9$ Estimate the mean weight of all apples of this variety.

There are 2140 students in a school district. In a sample of 449 students from this school district, 169 have mathematics scores below grade level. Based on this sample statistic, estimate the number of students in this school district with mathematics scores at or above grade level.

There are 341 teachers at a college. In a sample of 110 teachers from this college, 72 have doctorates. Based on this sample statistic, estimate the number of teachers at this college with doctorates.

There are 328 teachers at a college. In a sample of 111 teachers from this college, 75 have doctorates. Based on this sample statistic, estimate the number of teachers at this college without doctorates.

There are 13,417 eligible voters in one town. In a sample of 802 eligible voters from this town, 386 say that they plan to vote in the next mayoral election. Based on this sample statistic, estimate the number of eligible voters in this town who will not vote in the next mayoral election.

Eleven female college students are selected at random and asked their heights. The heights (in inches) are as follows: $68,59,65,71,64,63,68,63,61,65,62$ Estimate the mean height of all female students at this college.

There are 2221 students in a school district. In a sample of 452 students from this school district, 161 have mathematics scores below grade level. Based on this sample statistic, estimate the population proportion of students in this district with mathematics scores below grade level.

There are 13,427 eligible voters in one town. In a sample of 825 eligible voters from this town, the proportion who say that they plan to vote in the next mayoral election is 0.48 . Based on that sample statistic, what is the best estimate of the proportion for all eligible voters in the town?

In a survey of high school students, 1100 students were randomly selected from California, and the proportion who spoke a second language in addition to English was 0.15. Based on that sample statistic, what is the best Estimate of the proportion for all high school students in California?

There are 2030 students in a school district. In a sample of 483 students from this school district, 164 have mathematics scores below grade level. Based on this sample statistic, estimate the number of students in this school district with mathematics scores below grade level.