Question 1

Use the following to answer the questions below:
Identify if each of the following statements is a proper interpretation of a 95% confidence interval.
-I am 95% sure that this interval will contain the population parameter.

Accepted Answer

A 95% confidence interval is designed to have a 95% probability of containing the true population parameter.

Question 2

Use the following to answer the questions below:
Identify if each of the following statements is a proper interpretation of a 95% confidence interval.
-I am 95% sure that this interval will contain the sample statistic.

Accepted Answer

A 95% confidence interval is about the population parameter, not the sample statistic. It means that if we were to take many samples and build a confidence interval from each, 95% of those intervals would contain the true population parameter.

Question 3

Use the following to answer the questions below:
Identify if each of the following statements is a proper interpretation of a 95% confidence interval.
-95% of the population values will fall within this interval.

Accepted Answer

A 95% confidence interval means that if we were to take many samples and build a confidence interval from each sample, we would expect 95% of those intervals to contain the true population parameter, not that 95% of the population values fall within the interval.

Question 4

Use the following to answer the questions below:
Identify if each of the following statements is a proper interpretation of a 95% confidence interval.
-The probability that the population parameter is in this interval is 0.95.

Accepted Answer

A 95% confidence interval means that if we were to take many samples and build a confidence interval from each, about 95% of those intervals would contain the population parameter. It does not mean there is a 95% probability that the specific interval calculated from a single sample contains the parameter.

Question 5

Use the following to answer the questions below:
Identify if each of the following statements is a proper interpretation of a 95% confidence interval.
-95% of the possible samples from this population will have sample statistics in this particular interval.

Accepted Answer

A 95% confidence interval means that if we were to take many samples and build a confidence interval from each, about 95% of those intervals would contain the true population parameter, not that 95% of samples will have statistics in this interval.

Question 6

Recently, the Centers for Disease Control and Prevention estimated 9.4% of children under the age of 18 had asthma. They reported the standard error to be 0.35%. Assuming that the sampling distribution is symmetric and bell-shaped, find a 95% confidence interval.
A) 8.7% to 10.1%
B) 9.1% to 7.8%
C) 8.4% to 10.5%
D) 8.1% to 10.8%

Accepted Answer

0.094 ± 2 ? 0.0035 ? 0.094 ± 0.007 ? 0.087 to 0.101 (or, 8.7% to 10.1%)

Question 7

Use the following to answer the questions below:
A sample of 148 college students reports sleeping an average of 6.85 hours on weeknights, with a margin of error of 0.35 hours. Based on this information, identify each of the following as plausible or not for the average amount of sleep college students get on weeknights.
-6.6 hours
A) Plausible
B) Not plausible

Accepted Answer

The plausible range for the average amount of sleep is from 6.85 - 0.35 = 6.5 hours to 6.85 + 0.35 = 7.2 hours. Since 6.6 hours falls within this range, it is plausible.

Question 8

Use the following to answer the questions below:
A sample of 148 college students reports sleeping an average of 6.85 hours on weeknights, with a margin of error of 0.35 hours. Based on this information, identify each of the following as plausible or not for the average amount of sleep college students get on weeknights.
-7.5 hours
A) Plausible
B) Not plausible

Accepted Answer

The plausible range for the average amount of sleep is 6.85 ± 0.35 hours, which is 6.5 to 7.2 hours. Since 7.5 hours is outside this range, it is not plausible.

Question 9

Use the following to answer the questions below:
A sample of 148 college students reports sleeping an average of 6.85 hours on weeknights, with a margin of error of 0.35 hours. Based on this information, identify each of the following as plausible or not for the average amount of sleep college students get on weeknights.
-8 hours
A) Plausible
B) Not plausible

Accepted Answer

The average sleep reported is 6.85 hours with a margin of error of 0.35 hours, giving a range of 6.5 to 7.2 hours. 8 hours is outside this range, making it not plausible.

Question 10

Use the following to answer the questions below:
In a poll conducted before a Massachusetts city's mayoral election, 134 of 420 randomly chosen likely voters indicated that they planned to vote for the Democratic candidate.
-Compute a sample statistic from these data. Report your answer with three decimal places.

Accepted Answer

11eeb2d3_8e1d_6a63_b9aa_87f1cb40ab07_TBW1049_11 
 = 134/420 = 0.319

Question 11

Use the following to answer the questions below:
In a poll conducted before a Massachusetts city's mayoral election, 134 of 420 randomly chosen likely voters indicated that they planned to vote for the Democratic candidate.
-Suppose that an article describing the poll says that the margin of error for the statistic is 0.045. Use this information to find an interval estimate. Report your answer with three decimal places.

Accepted Answer

0.319 ± 0.045 ? 0.274 to 0.364

Question 12

Use the following to answer the questions below:
In a poll conducted before a Massachusetts city's mayoral election, 134 of 420 randomly chosen likely voters indicated that they planned to vote for the Democratic candidate.
-Suppose that an article describing the poll says that the margin of error for the statistic is 0.045 and an interval estimate is found.What quantity is the interval estimate in trying to capture? Identify with appropriate notation and words.
A) p = proportion of likely voters who plan to vote for the Democratic candidate
B)    = proportion of likely voters who plan to vote for the Democratic candidate
C) $\mu$ = the mean number of voters who plan to vote for the Democratic candidate
D)    = the mean number of voters who plan to vote for the Democratic candidate

Accepted Answer

The answer of Use the following to answer the questions...

Question 13

Use the following to answer the questions below:
In a poll conducted before a Massachusetts city's mayoral election, 134 of 420 randomly chosen likely voters indicated that they planned to vote for the Democratic candidate.
-Suppose that an article describing the poll says that the margin of error for the statistic is 0.045. Use this information to find an interval estimate and interpret the confidence interval.

Accepted Answer

The answer of Use the following to answer the questions...

Question 14

Use the following to answer the questions below:
In a poll conducted before a Massachusetts city's mayoral election, 134 of 420 randomly chosen likely voters indicated that they planned to vote for the Democratic candidate.
-Suppose that a student collects pulse rates from a random sample of 200 students at her college and finds a 90% confidence interval goes from 65.5 to 71.8 beats per minute. Is the following statement an appropriate interpretation of this interval? If not, explain why not.
"90% of the students at my college have mean pulse rates between 65.5 and 71.8 beats per minute."

Accepted Answer

The answer of Use the following to answer the questions...

Question 15

Use the following to answer the questions below:
Identify whether each of the following samples is a possible bootstrap sample from this original sample: 20, 24, 19, 23, 18
-24, 18, 23

Accepted Answer

The answer of Use the following to answer the questions...

Question 16

Use the following to answer the questions below:
Identify whether each of the following samples is a possible bootstrap sample from this original sample: 20, 24, 19, 23, 18
-24, 19, 24, 20,23

Accepted Answer

Bootstrap samples are created by sampling with replacement from the original sample, so any combination of the original sample values is possible, including repeated values.

Question 17

Use the following to answer the questions below:
Identify whether each of the following samples is a possible bootstrap sample from this original sample: 20, 24, 19, 23, 18
-20, 24, 21, 19, 18

Accepted Answer

The answer of Use the following to answer the questions...

Question 18

Use the following to answer the questions below:
Identify whether each of the following samples is a possible bootstrap sample from this original sample: 20, 24, 19, 23, 18
-20, 20, 20, 20, 20

Accepted Answer

A bootstrap sample is created by randomly sampling with replacement from the original sample, so repeating values like "20" multiple times is possible.

Question 19

Use the following to answer the questions below:
Identify whether each of the following samples is a possible bootstrap sample from this original sample: 20, 24, 19, 23, 18
-18, 19, 20, 23, 24

Accepted Answer

A bootstrap sample is created by randomly sampling with replacement from the original sample, so duplicates and different orders are possible.

Question 20

A sample of size 46 with a mean of 13.6 is to be used to construct a confidence interval for ?. A bootstrap distribution based on 1,000 samples is created. Where will the bootstrap distribution be centered?
A) 46
B) 13.6
C) $\mu$
D) 1,000

Accepted Answer

The bootstrap distribution is centered around the sample mean, which is 13.6 in this case.

Quiz 3: Confidence Intervals

Use the following to answer the questions below: Identify if each of the following statements is a proper interpretation of a 95% confidence interval. -I am 95% sure that this interval will contain the population parameter.

Use the following to answer the questions below: Identify if each of the following statements is a proper interpretation of a 95% confidence interval. -I am 95% sure that this interval will contain the sample statistic.

Use the following to answer the questions below: Identify if each of the following statements is a proper interpretation of a 95% confidence interval. -95% of the population values will fall within this interval.

Use the following to answer the questions below: Identify if each of the following statements is a proper interpretation of a 95% confidence interval. -The probability that the population parameter is in this interval is 0.95.

Use the following to answer the questions below: Identify if each of the following statements is a proper interpretation of a 95% confidence interval. -95% of the possible samples from this population will have sample statistics in this particular interval.

Recently, the Centers for Disease Control and Prevention estimated 9.4% of children under the age of 18 had asthma. They reported the standard error to be 0.35%. Assuming that the sampling distribution is symmetric and bell-shaped, find a 95% confidence interval.

Use the following to answer the questions below: Identify whether each of the following samples is a possible bootstrap sample from this original sample: 20, 24, 19, 23, 18 -24, 18, 23

Use the following to answer the questions below: Identify whether each of the following samples is a possible bootstrap sample from this original sample: 20, 24, 19, 23, 18 -24, 19, 24, 20,23

Use the following to answer the questions below: Identify whether each of the following samples is a possible bootstrap sample from this original sample: 20, 24, 19, 23, 18 -20, 24, 21, 19, 18

Use the following to answer the questions below: Identify whether each of the following samples is a possible bootstrap sample from this original sample: 20, 24, 19, 23, 18 -20, 20, 20, 20, 20

Use the following to answer the questions below: Identify whether each of the following samples is a possible bootstrap sample from this original sample: 20, 24, 19, 23, 18 -18, 19, 20, 23, 24

A sample of size 46 with a mean of 13.6 is to be used to construct a confidence interval for ?. A bootstrap distribution based on 1,000 samples is created. Where will the bootstrap distribution be centered?