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Question 1

The population standard deviation in the sales of bikes per day of an

automobile company is known to be 3 bikes per day. A random sample

of 47 days has a mean sales of 5 bikes per day. Identify the distribution

that can be used to construct a confidence interval for the mean sales

per day:

Group of answer choices

A. The distribution that can be used in constructing a confidence

interval is the Chi-square distribution with (n-1) degrees of freedom

B. The distribution that can be used in constructing a confidence

interval is the normal distribution with mean and standard deviation > 0

C. The distribution that can be used in constructing a confidence

interval is the standard normal distribution

D. The distribution that can be used in constructing a confidence

interval is the t distribution with (n-1) degrees of freedom

E. The distribution that can be used in constructing a confidence

interval is the F distribution

Question 2

A random variable X takes on the following values and probabilities:

X

1

2

3

4

P(X=x)

0.07

0.22

0.09

0.62

Find the mean value of X.

If rounding is needed, round only once you have completed all

calculations (to two decimals, example answer: 1.23).

Question 3

Let X be the number of problems solved in a single day (along with their

associated probabilities).

X

1

6

11

18

21

P(X=x)

0.18

0.32

0.28

0.12

0.1

Calculate the variance and standard deviation for the random variable

X:

If rounding is needed, round only once you have completed all

calculations (to two decimals, example answer: 1.23).

Question 4

The duration of a cricket match is normally distributed with a mean of

182 minutes and a standard deviation of 9 minutes. Find the probability

that a cricket match is completed within 180 minutes

Group of answer choices

A. The probability that a cricket match is completed within 180 minutes

is 0.588

B. The probability that a cricket match is completed within 180 minutes

is 0.222

C. The probability that a cricket match is completed within 180 minutes

is 0.788

D. The probability that a cricket match is completed within 180 minutes

is 0.412

E. The probability that a cricket match is completed within 180 minutes

is 0.500

Question 5

A student claims that the average audience size of sports events is

significantly different from 190 in his school. He samples 30 sports

events, and the average audience size is 220. We already know the

standard deviation of audience size of sports events in his school is 25.

Test the student’s claim at 90% confidence level by using both the

confidence interval and hypothesis testing methods. What is the decision

in terms of the null hypothesis by both the methods?

Group of answer choices

A. The null hypothesis is rejected, and the student is correct in her claim

by using both the hypothesis and confidence interval methods.

B. The null hypothesis is rejected, and the student is not correct in her

claim by using both the hypothesis and confidence interval methods.

C. The null hypothesis is not rejected, and the student is correct in her

claim by using both the hypothesis and confidence interval methods.

D. The null hypothesis is not rejected, and the student is not correct in

her claim by using both the hypothesis and confidence interval methods.

Question 6

The average waiting time duration in a medical clinic is assumed to be 45

minutes with a standard deviation of 10 minutes. A researcher

conducted a hypothesis test to test whether the average waiting time is

more than 45 minutes. The test statistic value is found to be

1.907. Given an interpretation of the test at 0.01 (1%) level of

significance:

Group of answer choices

A. The null hypothesis is rejected and there is insufficient evidence to

conclude that the average waiting time duration in the medical clinic is

more than 45 minutes

B. The null hypothesis is rejected and there is sufficient evidence to

conclude that the average waiting time duration in the medical clinic is

more than 45 minutes

C. The null hypothesis is not rejected and there is insufficient evidence

to conclude that the average waiting time duration in the medical clinic is

more than 45 minutes

D. The null hypothesis is not rejected and there is sufficient evidence to

conclude that the average waiting time duration in the medical clinic is

more than 45 minutes

Question 7

To test H0:μ≥40,Ha:μ0.04

E. H0:p≤0.04Ha:p>0.04

F. H0:μ≤0.04Ha:μ>0.04

Question 10

In a private hospital, the director claimed that they provide all the

essentials to the nurses for their work (in terms of medical equipment,

travel facilities, etc.) and that exactly 90% (no more or less) of the nurses

are satisfied with the essentials provided by the hospital. 79 nurses were

sampled and asked whether they are satisfied with the essentials in the

hospital — 7 nurses said they were not. Find the appropriate test statistic

and p-value for this test.

Group of answer choices

A.

B.

C.

D.

The test statistic is 0.34 and the p-value is 0.7339

The test statistic is 0.34 and the p-value is 0.3669

The test statistic is 0.34 and the p-value is 0.633

The test statistic is 0.34 and the p-value is 0.367

Question 11

The 95% confidence interval for the proportion of students who work in

part time jobs is (0.0815, 0.1785). The sample proportion of students

who work in part time jobs is known to be 0.13. What sample size is used

to obtain the confidence interval: (Only round at the end of your

calculation to nearest whole number. Example answer: 137)

Question 12

A researcher claims that the proportion of athlete fatalities related to

alcohol is less than 24%. In a random sample of 35 athlete fatalities, it

was found that 17% of deaths were caused by alcohol. Test the claim at

alpha = 1%

Group of answer choices

A. More information is needed to test the claim

B. There is not enough evidence to conclude that the proportion of

athlete fatalities related to alcohol is greater than 24%

C. There is sufficient evidence to conclude that the proportion of athlete

fatalities related to alcohol is greater than 24%

D. There is not enough evidence to conclude that the proportion of

athlete fatalities related to alcohol is less than 24%

E. There is sufficient evidence to conclude that the proportion of athlete

fatalities related to alcohol is less than 24%

Question 13

The upper limit of a 99% confidence interval for the mean is known to be

45.4 and the standard error is 3.7. If the population standard deviation is

known, find the lower limit of the given confidence interval:

Group of answer choices

A.

B.

C.

D.

The lower limit of the confidence interval is 26.35

The lower limit of the confidence interval is 35.87

The lower limit of the confidence interval is 36.79

The lower limit of the confidence interval is 28.19

Question 14

The 99% confidence interval for the mean number of road accidents per

day in a country is known as (14.3, 19.3). Is there sufficient evidence to

conclude that the mean number of accidents is 17.4 per day?

Group of answer choices

A. The null hypothesis is rejected and there is insufficient evidence to

conclude that the mean number of accidents is 17.4 per day

B. The null hypothesis is not rejected and there is insufficient evidence

to conclude that the mean number of accidents is 17.4 per day

C. The null hypothesis is not rejected and it’s possible that the mean

number of accidents is 17.4 per day

D. The null hypothesis is rejected and it’s possible that the mean

number of accidents is 17.4 per day

E. There is not enough information provided to make a decision for a

hypothesis test

Question 15

The 95% confidence interval for the proportion of people who support

the new budget scheme is (0.34 – 0.60). Find the margin of error and

standard error of this estimate.

Group of answer choices

A. The margin of error is 0.130 and the standard error of the estimate is

0.0663

B. The margin of error is 0.130 and the standard error of the estimate is

0.0790

C. The margin of error is 0.260 and the standard error of the estimate is

0.0663

D. The margin of error is 0.260 and the standard error of the estimate is

0.0790

Question 16

In a sample of 400 high school students, the proportion of students who

support a new teaching method is 0.25. Give an interpretation for a 99%

confidence interval for the proportion of students who support the new

teaching method.

Group of answer choices

A. There is 99% confidence that the sample proportion of students who

support the new teaching method lies between 0.1941 and 0.3059

B. There is 99% confidence that the population proportion of students

who support the new teaching method lies between 0.1941 and 0.3059

C. There is 99% confidence that the sample proportion of students who

support the new teaching method lies between 0.1996 and 0.3004

D. There is 99% confidence that the population proportion of students

who support the new teaching method lies between 0.1996 and 0.3004

Question 17

Which of the following is inversely proportional to the width of the

confidence interval for proportions?

Group of answer choices

A. Confidence level is inversely proportional to the width of the

confidence interval for proportions

B. Sample size is inversely proportional to the width of the confidence

interval for proportions

C. Standard Error is inversely proportional to the width of the

confidence interval for proportions

D. Sample proportion (00.04

F. H0:μ≤0.04Ha:μ>0.04

Question 10

In a private hospital, the director claimed that they provide all the

essentials to the nurses for their work (in terms of medical equipment,

travel facilities, etc.) and that exactly 90% (no more or less) of the nurses

are satisfied with the essentials provided by the hospital. 79 nurses were

sampled and asked whether they are satisfied with the essentials in the

hospital — 7 nurses said they were not. Find the appropriate test statistic

and p-value for this test.

Group of answer choices

A.

B.

C.

D.

The test statistic is 0.34 and the p-value is 0.7339

The test statistic is 0.34 and the p-value is 0.3669

The test statistic is 0.34 and the p-value is 0.633

The test statistic is 0.34 and the p-value is 0.367

Question 11

The 95% confidence interval for the proportion of students who work in

part time jobs is (0.0815, 0.1785). The sample proportion of students

who work in part time jobs is known to be 0.13. What sample size is used

to obtain the confidence interval: (Only round at the end of your

calculation to nearest whole number. Example answer: 137)

Question 12

A researcher claims that the proportion of athlete fatalities related to

alcohol is less than 24%. In a random sample of 35 athlete fatalities, it

was found that 17% of deaths were caused by alcohol. Test the claim at

alpha = 1%

Group of answer choices

A. More information is needed to test the claim

B. There is not enough evidence to conclude that the proportion of

athlete fatalities related to alcohol is greater than 24%

C. There is sufficient evidence to conclude that the proportion of athlete

fatalities related to alcohol is greater than 24%

D. There is not enough evidence to conclude that the proportion of

athlete fatalities related to alcohol is less than 24%

E. There is sufficient evidence to conclude that the proportion of athlete

fatalities related to alcohol is less than 24%

Question 13

The upper limit of a 99% confidence interval for the mean is known to be

45.4 and the standard error is 3.7. If the population standard deviation is

known, find the lower limit of the given confidence interval:

Group of answer choices

A.

B.

C.

D.

The lower limit of the confidence interval is 26.35

The lower limit of the confidence interval is 35.87

The lower limit of the confidence interval is 36.79

The lower limit of the confidence interval is 28.19

Question 14

The 99% confidence interval for the mean number of road accidents per

day in a country is known as (14.3, 19.3). Is there sufficient evidence to

conclude that the mean number of accidents is 17.4 per day?

Group of answer choices

A. The null hypothesis is rejected and there is insufficient evidence to

conclude that the mean number of accidents is 17.4 per day

B. The null hypothesis is not rejected and there is insufficient evidence

to conclude that the mean number of accidents is 17.4 per day

C. The null hypothesis is not rejected and it’s possible that the mean

number of accidents is 17.4 per day

D. The null hypothesis is rejected and it’s possible that the mean

number of accidents is 17.4 per day

E. There is not enough information provided to make a decision for a

hypothesis test

Question 15

The 95% confidence interval for the proportion of people who support

the new budget scheme is (0.34 – 0.60). Find the margin of error and

standard error of this estimate.

Group of answer choices

A. The margin of error is 0.130 and the standard error of the estimate is

0.0663

B. The margin of error is 0.130 and the standard error of the estimate is

0.0790

C. The margin of error is 0.260 and the standard error of the estimate is

0.0663

D. The margin of error is 0.260 and the standard error of the estimate is

0.0790

Question 16

In a sample of 400 high school students, the proportion of students who

support a new teaching method is 0.25. Give an interpretation for a 99%

confidence interval for the proportion of students who support the new

teaching method.

Group of answer choices

A. There is 99% confidence that the sample proportion of students who

support the new teaching method lies between 0.1941 and 0.3059

B. There is 99% confidence that the population proportion of students

who support the new teaching method lies between 0.1941 and 0.3059

C. There is 99% confidence that the sample proportion of students who

support the new teaching method lies between 0.1996 and 0.3004

D. There is 99% confidence that the population proportion of students

who support the new teaching method lies between 0.1996 and 0.3004

Question 17

Which of the following is inversely proportional to the width of the

confidence interval for proportions?

Group of answer choices

A. Confidence level is inversely proportional to the width of the

confidence interval for proportions

B. Sample size is inversely proportional to the width of the confidence

interval for proportions

C. Standard Error is inversely proportional to the width of the

confidence interval for proportions

D. Sample proportion (00.04

F. H0:μ≤0.04Ha:μ>0.04

Question 10

In a private hospital, the director claimed that they provide all the

essentials to the nurses for their work (in terms of medical equipment,

travel facilities, etc.) and that exactly 90% (no more or less) of the nurses

are satisfied with the essentials provided by the hospital. 79 nurses were

sampled and asked whether they are satisfied with the essentials in the

hospital — 7 nurses said they were not. Find the appropriate test statistic

and p-value for this test.

Group of answer choices

A.

B.

C.

D.

The test statistic is 0.34 and the p-value is 0.7339

The test statistic is 0.34 and the p-value is 0.3669

The test statistic is 0.34 and the p-value is 0.633

The test statistic is 0.34 and the p-value is 0.367

Question 11

The 95% confidence interval for the proportion of students who work in

part time jobs is (0.0815, 0.1785). The sample proportion of students

who work in part time jobs is known to be 0.13. What sample size is used

to obtain the confidence interval: (Only round at the end of your

calculation to nearest whole number. Example answer: 137)

Question 12

A researcher claims that the proportion of athlete fatalities related to

alcohol is less than 24%. In a random sample of 35 athlete fatalities, it

was found that 17% of deaths were caused by alcohol. Test the claim at

alpha = 1%

Group of answer choices

A. More information is needed to test the claim

B. There is not enough evidence to conclude that the proportion of

athlete fatalities related to alcohol is greater than 24%

C. There is sufficient evidence to conclude that the proportion of athlete

fatalities related to alcohol is greater than 24%

D. There is not enough evidence to conclude that the proportion of

athlete fatalities related to alcohol is less than 24%

E. There is sufficient evidence to conclude that the proportion of athlete

fatalities related to alcohol is less than 24%

Question 13

The upper limit of a 99% confidence interval for the mean is known to be

45.4 and the standard error is 3.7. If the population standard deviation is

known, find the lower limit of the given confidence interval:

Group of answer choices

A.

B.

C.

D.

The lower limit of the confidence interval is 26.35

The lower limit of the confidence interval is 35.87

The lower limit of the confidence interval is 36.79

The lower limit of the confidence interval is 28.19

Question 14

The 99% confidence interval for the mean number of road accidents per

day in a country is known as (14.3, 19.3). Is there sufficient evidence to

conclude that the mean number of accidents is 17.4 per day?

Group of answer choices

A. The null hypothesis is rejected and there is insufficient evidence to

conclude that the mean number of accidents is 17.4 per day

B. The null hypothesis is not rejected and there is insufficient evidence

to conclude that the mean number of accidents is 17.4 per day

C. The null hypothesis is not rejected and it’s possible that the mean

number of accidents is 17.4 per day

D. The null hypothesis is rejected and it’s possible that the mean

number of accidents is 17.4 per day

E. There is not enough information provided to make a decision for a

hypothesis test

Question 15

The 95% confidence interval for the proportion of people who support

the new budget scheme is (0.34 – 0.60). Find the margin of error and

standard error of this estimate.

Group of answer choices

A. The margin of error is 0.130 and the standard error of the estimate is

0.0663

B. The margin of error is 0.130 and the standard error of the estimate is

0.0790

C. The margin of error is 0.260 and the standard error of the estimate is

0.0663

D. The margin of error is 0.260 and the standard error of the estimate is

0.0790

Question 16

In a sample of 400 high school students, the proportion of students who

support a new teaching method is 0.25. Give an interpretation for a 99%

confidence interval for the proportion of students who support the new

teaching method.

Group of answer choices

A. There is 99% confidence that the sample proportion of students who

support the new teaching method lies between 0.1941 and 0.3059

B. There is 99% confidence that the population proportion of students

who support the new teaching method lies between 0.1941 and 0.3059

C. There is 99% confidence that the sample proportion of students who

support the new teaching method lies between 0.1996 and 0.3004

D. There is 99% confidence that the population proportion of students

who support the new teaching method lies between 0.1996 and 0.3004

Question 17

Which of the following is inversely proportional to the width of the

confidence interval for proportions?

Group of answer choices

A. Confidence level is inversely proportional to the width of the

confidence interval for proportions

B. Sample size is inversely proportional to the width of the confidence

interval for proportions

C. Standard Error is inversely proportional to the width of the

confidence interval for proportions

D. Sample proportion (0

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