6. Match each of the following statements with the terms and values below:

1.The sampling distribution of the sample mean becomes approximately normal asnnbecomes large

2. (Upper confidence limit - Lower confidence limit)/2

3. A single statistic that is used to estimate a population parameter

4. RejectingH0:29when in fact=27

5. Failure to reject a false null hypothesis

6. If we fail to rejectH0at=0.03we must also fail to reject it at

7. A range of values of a sample statistic that likely contains the population parameter

8.If we rejectH0at=0.05we must also reject it at

9. The decision when the test statistic falls outside the critical region

10. 1 -

1. Confidence level
2. Margin of Error
3. =0.015
4. Type I error
5. Confidence interval
6. =0.08
7. Central Limit Theorem
8. Point estimate
9. Fail to rejectH0
10. Type II error

8. A professor wants to estimate how long students stay connected during two-hour online lectures. From a random sample of 24 students, the mean stay time was 82 minutes with a standard deviation of 14 minutes.

Assuming the population has a normal distribution, develop a 95% confidence interval estimate for the population mean by determining the following values:

1. a) Point Estimate =

b) df =Significance level () =

c) Determine the critical value rounded to 3 decimal places. Enter a positive value.

[3 decimal places] Critical value =

d) [3 decimal places] Standard Error =

e) [1 decimal place] Margin of Error =

f) [1 decimal place] Lower Confidence Limit =

g) [1 decimal place] Upper Confidence Limit =

2. Should we reject a claim that the population mean, = 69 minutes? Why?

3. If the sample size decreases, what will be the effect on the margin of error?

11.On a peer-to-peer (P2P) lending website, borrowers complete a approval scoring form that lenders use to assess creditworthiness. Borrowers are rated A, B, C or D, based on their scores, with A having the highest scores and D having the lowest.

In a large sample of borrowers, 19% were rated A, 32% were rated B, 24% were rated C, and the rest were rated D. Suppose the scores are normally distributed with a mean of 313 and a standard deviation of 49.

Round numeric answers to the nearest integer.

a) What is the cut-off score between A and B?

b) What is the cut-off score between B and C?

c) What is the cut-off score between C and D?

d) What score corresponds to the 25th percentile?

e) What score corresponds to the 75th percentile?

f) What is the minimum score above which lies 16% of the scores?

g) Between what scores will the middle 86% of scores lie?

Lower value = Higher value =

h) What rating will a score of 350 receive?Select an answer

D-rating

C-rating

B-rating

A-rating

i) What rating will a score of 271 receive?Select an answer

D-rating

C-rating

B-rating

A-rating

9.In constructing a confidence interval for a population mean, which of the following are true?

Select four (4) true statements from the list below:

• A point estimate is a single population parameter that is used to a estimate a sample statistic.
• The width of the confidence interval depends on the size of the confidence level.
• If a confidence interval does not contain the population parameter, then an error has been made in the calculation.
• If a confidence interval for the population mean is constructed from a sample of sizen
• =
• 30
• n=30
• , that interval must contain the sample mean.
• Decreasing the confidence level will increase the width of the confidence interval.
• A 97% confidence interval must capture 97% of the population values.
• For the same sample data, a 95% confidence interval will be wider than a 99% confidence interval.
• If the point estimate and upper limit for a confidence interval are 170.1 and 182.1 respectively, then the lower limit must be 12.
• If a particular 85% confidence interval captures the population mean, then for the same sample data, the population mean will also be captured at the 87% confidence level.
• Increasing the sample size will decrease the width of the confidence interval.
• For a confidence level of 97%, the right-tail area
• /2 = 0.06.
• A confidence interval that fails to capture the population mean will also fail to capture the sample mean.

10.Which of the following statements about the sampling distribution of the mean (distribution of sample means) and the central limit theorem (CLT) are true?

Select four (4) true statements from the list below:

• The smaller the sample size, the smaller the difference between the mean of the sampling distribution and the population mean.
• The sampling distribution is always approximately normal even if the population is not normal.
• From the same population, the standard error of the sampling distribution withn
• n
• = 14 will be the same as the standard error withn
• n
• = 38.
• If the population is approximately normally distributed, then sample size does not matter for the central limit theorem to apply.
• From the same population, the mean of the sampling distribution (
• x
• x
• ) withn
• n
• = 7 will be the same as the mean withn
• n
• = 17.
• The smaller the sample size, the larger the standard error.
• If
• x
• =
• x=
• and
• x
• =
• n
• x=n
• , then the distribution of sample means is normal.
• The sampling distribution of the mean will be approximately normal when
• is large.
• The sampling distribution is still assumed to be approximately normal if the underlying population is bimodal as long as the sample size is large.
• The shape of the sampling distribution is closer to the population shape as the sample size increases.
• If a population is perfectly normal, then for the distribution of sample means of any size,
• x
• =
• x=
• and
• x
• =
• x=
• .