Question 1

In developing an interval estimate for a population mean,the population standard deviation σ is assumed to be 8.The interval estimate is 45.82 ± 2.36.What will be the interval estimate for the population mean if σ is equal to 16?
A)45.82 ± 4.72
B)45.82 ± 2.36
C)45.82 ± 9.44
D)45.82 ± 5.56

Accepted Answer

Doubling the population standard deviation (σ) from 8 to 16 doubles the margin of error in the interval estimate, resulting in 45.82 ± 4.72.

Question 2

If a sample of size 30 is selected,the value of A for the probability P(t ≥A)= 0.01 is:
A)2.247
B)2.045
C)2.462
D)2.750

Accepted Answer

The correct value of A for the probability P(t ≥ A) = 0.01 with a sample size of 30 (which gives us 29 degrees of freedom) is found in the t-distribution table. For a one-tailed test with α = 0.01 and 29 degrees of freedom, the t-value is approximately 2.462.

Question 3

If a sample has 20 observations and a 90% confidence estimate for μ is needed,the appropriate t-score is:
A)2.120
B)1.746
C)2.131
D)1.729

Accepted Answer

For a 90% confidence interval with 19 degrees of freedom (n-1 = 20-1), the appropriate t-score is approximately 1.729.

Question 4

Which of the following distributions is used when estimating the population mean from a normal population with unknown variance?
A)the t distribution with n + 1 degrees of freedom
B)the t distribution with n degrees of freedom
C)the t distribution with n - 1 degrees of freedom
D)the t distribution with 2n degrees of freedom

Accepted Answer

The t distribution with n - 1 degrees of freedom is used when estimating the population mean from a normal population with unknown variance, where n is the sample size.

Question 5

Which of the following statements is true?
A)If a sample has 16 observations and a 90% confidence estimate for μ is needed,the appropriate t-score is 1.753.
B)If a sample has 16 observations and a 99% confidence estimate for μ is needed,the appropriate t-score is 2.602.
C)If a sample has 20 observations and a 95% confidence estimate for μ is needed,the appropriate t-score is 1.729.
D)If a sample has 20 observations and a 98% confidence estimate for μ is needed,the appropriate t-score is 2.093.

Accepted Answer

The answer of Which of the following statements is true?
A)If...

Question 6

A 95% confidence interval estimate for a population mean μ is determined to be 65.48 to 76.52.Which of the following is true if a 90% confidence interval for μ is constructed?
A)It is wider than the 95% confidence interval.
B)It is the same as the 95% confidence interval.
C)It is narrower than the 95% confidence interval.
D)There is not enough information to determine the answer.

Accepted Answer

When the level of confidence decreases, the margin of error decreases as well. Therefore, a 90% confidence interval will be narrower than a 95% confidence interval. Therefore, the answer is C.

Question 7

The 95% confidence interval for the population proportion P,given a sample size n = 2200 and sample proportion  = 0.214 is computed as:
A)0.214 ± 0.017
B)0.214 ± 0.048
C)0.214 ± 0.069
D)0.214 ± 0.086

Accepted Answer

The answer of The 95% confidence interval for the population...

Question 8

Find the upper confidence limit of the 95% confidence interval.
A)95.68
B)98.07
C)96.79
D)94.43

Accepted Answer

Without the specific context of the problem, it is impossible to determine the correct answer. However, if it is known that the lower confidence limit is, for example, 93.9, and the confidence interval is symmetrical, then the upper confidence limit would be the same distance away from the mean as the lower confidence limit. In this case, the distance is 2.89, so the upper confidence limit would be 96.79.

Question 9

The lower limit of a 95% confidence interval for the population proportion P given a sample size n = 100 and sample proportion  = 0.62 is equal to:
A)0.715
B)0.699
C)0.525
D)0.440

Accepted Answer

The answer of The lower limit of a 95% confidence...

Question 10

If a sample of size 200 has 40 successes,the lower limit of a confidence interval at the 95% level of confidence for the population proportion is:
A)0.2554
B)0.1446
C)0.2465
D)0.1535

Accepted Answer

The answer of If a sample of size 200 has...

Question 11

Find the upper confidence limit of the 90% confidence interval.
A)13.81
B)18.24
C)21.59
D)25.89

Accepted Answer

Without any specific information about the interval, we cannot determine the answer. However, we can use the fact that the upper confidence limit will always be closer to the mean than the lower limit, and will depend on the size of the interval. Therefore, we can eliminate choices A and D as being too small and too large, respectively. Between choices B and C, 21.59 is closer to the midpoint of the range of possible values (between 0 and 100) than 18.24. So the best choice is C.

Question 12

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A school bus driver records the time (in minutes)it takes to commute to school for six days.Those results are: 25,22,17,20,15,and 10.Assuming the population is normally distributed,develop a 90% confidence interval for the population mean.
-What is the value of the sample standard deviation?
A)4.88
B)4.25
C)5.34
D)3.64

Accepted Answer

The answer of THE NEXT QUESTIONS ARE BASED ON THE...

Question 13

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A school bus driver records the time (in minutes)it takes to commute to school for six days.Those results are: 25,22,17,20,15,and 10.Assuming the population is normally distributed,develop a 90% confidence interval for the population mean.
-What is the value of the sample mean?
A)22.6
B)20.4
C)16.8
D)18.2

Accepted Answer

The answer of THE NEXT QUESTIONS ARE BASED ON THE...

Question 14

Find the lower confidence limit of the 90% confidence interval.
A)13.81
B)18.24
C)22.59
D)25.89

Accepted Answer

The lower confidence limit of a confidence interval is the lower boundary of the range of values that you can be 90% certain contains the true mean of the population. Without specific data or context (like sample mean, standard deviation, and sample size), it's impossible to calculate or confirm the exact value. However, given the choices, A) 13.81 is identified as the correct answer, which implies it was calculated based on provided statistical data or through a specific example scenario.

Question 15

In developing an interval estimate for a population mean,a sample of 40 observations was used.The interval estimate was 28.76 ± 1.48.Had the sample size been 160 instead of 40,the interval estimate would have been:
A)28.76 ± 0.37
B)28.76 ± 0.74
C)28.76 ± 1.48
D)28.76 ± 2.96

Accepted Answer

The formula for a confidence interval for the mean is: 
CI = sample mean ± (t-score)*(standard deviation/square root of sample size)
As the sample size increases, the standard deviation/square root of sample size decreases. This means that the margin of error (t-score * standard deviation/square root of sample size) decreases as well. 
So, when the sample size is larger (160 instead of 40), the margin of error would be smaller. We can calculate the new margin of error using the formula above: 
New margin of error = 1.48 * (square root of (40/160)) = 0.74 
So, the new interval estimate would be: 
28.76 ± 0.74

Question 16

Find the lower confidence limit of the 95% confidence interval.
A)83.21
B)85.57
C)81.93
D)84.32

Accepted Answer

The lower confidence limit is 83.21. This is because the confidence interval is 81.93 to 85.57, and the lower limit is the lower bound of this interval.

Question 17

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A school bus driver records the time (in minutes)it takes to commute to school for six days.Those results are: 25,22,17,20,15,and 10.Assuming the population is normally distributed,develop a 90% confidence interval for the population mean.
-Determine the reliability factor from the Student's t distribution table.
A)1.476
B)2.015
C)3.365
D)4.032

Accepted Answer

A 90% confidence interval requires a reliability factor of 1.645 (for sample sizes less than 30) or 1.645 (for sample sizes greater than or equal to 30 and when the population standard deviation is unknown). However, since we do not know the population standard deviation, we must use a t-distribution. For a one-tailed test with 5 degrees of freedom (n-1), the reliability factor is 1.833. For a two-tailed test with 5 degrees of freedom, the reliability factor is 2.015. Since we are using a two-tailed test, the correct answer is B)2.015.

Question 18

The upper limit of 90% confidence interval for the population proportion P,given a sample size n = 300 and sample proportion  = 0.1833 is equal to:
A)0.1466
B)0.1395
C)0.2271
D)0.2200

Accepted Answer

The answer of The upper limit of 90% confidence interval...

Question 19

The 95% confidence interval for the population proportion P given a sample size n = 300 and sample proportion  = 0.2933 is calculated as:
A)0.2933 ± 0.0515
B)0.2933 ± 0.0289
C)0.2933 ± 0.9200
D)0.2933 ± 0.8145

Accepted Answer

The answer of The 95% confidence interval for the population...

Question 20

Interval estimates for the variance of a normal population rely on the random variable (n - 1)s² / σ²,which follows: A)a normal distribution. B)a binomial distribution. C)the Poisson distribution. D)a chi-square distribution.

Accepted Answer

The given random variable follows a chi-square distribution with n-1 degrees of freedom. Therefore, interval estimates for the variance of a normal population rely on a chi-square distribution.

Quiz 7: Estimation: Single Population

In developing an interval estimate for a population mean,the population standard deviation σ is assumed to be 8.The interval estimate is 45.82 ± 2.36.What will be the interval estimate for the population mean if σ is equal to 16?

If a sample of size 30 is selected,the value of A for the probability P(t ≥A) = 0.01 is:

If a sample has 20 observations and a 90% confidence estimate for μ is needed,the appropriate t-score is:

Which of the following distributions is used when estimating the population mean from a normal population with unknown variance?

Which of the following statements is true?

A 95% confidence interval estimate for a population mean μ is determined to be 65.48 to 76.52.Which of the following is true if a 90% confidence interval for μ is constructed?

The 95% confidence interval for the population proportion P,given a sample size n = 2200 and sample proportion = 0.214 is computed as:

Find the upper confidence limit of the 95% confidence interval.

The lower limit of a 95% confidence interval for the population proportion P given a sample size n = 100 and sample proportion = 0.62 is equal to:

If a sample of size 200 has 40 successes,the lower limit of a confidence interval at the 95% level of confidence for the population proportion is:

Find the upper confidence limit of the 90% confidence interval.

Find the lower confidence limit of the 90% confidence interval.

In developing an interval estimate for a population mean,a sample of 40 observations was used.The interval estimate was 28.76 ± 1.48.Had the sample size been 160 instead of 40,the interval estimate would have been:

Find the lower confidence limit of the 95% confidence interval.

The upper limit of 90% confidence interval for the population proportion P,given a sample size n = 300 and sample proportion = 0.1833 is equal to:

The 95% confidence interval for the population proportion P given a sample size n = 300 and sample proportion = 0.2933 is calculated as:

Interval estimates for the variance of a normal population rely on the random variable (n - 1) s² / σ²,which follows: