Lessons 7.1 & 7.2 Partner Content Check

Last updated almost 2 years ago

14 questions

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Library

Lessons 7.1 & 7.2 Partner Content Check

Last updated almost 2 years ago

14 questions

Required

1

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2

Calculate the point estimate and margin of error used to create the confidence interval in #1.
Point estimate = _______ 
Margin of Error = _______ 

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2

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1

The Pew Research Center and Smithsonian magazine recently quizzed a random sample of 1006 U.S. adults on their knowledge of science.
One of the questions asked, “Which is the better way to determine whether a new drug is effective in treating a disease?
If a scientist has a group of 1000 volunteers with the disease to study, should she
(a) Give the drug to all of them and see how many get better or
(b) Give the drug to half of them and not to the other half, and compare how many in each group get better?”

A 95% confidence interval for the proportion of U.S. adults who would correctly answer (b) is 0.723 to 0.777.
Interpret this confidence interval. Use the sentence frame from our notes.
I will grade your answer to this question by hand.

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2

Calculate the point estimate and margin of error used to create the confidence interval in #4.
Point estimate = _______ 
Margin of Error = _______ 

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2

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2

A magazine reported that 66% of all dog owners usually greet their dog before greeting their spouse or children when they return home at the end of the workday. 
Researchers select 40 dog owners at random and ask them whom they greet first when returning home. 
The 95% confidence interval for the proportion of owners who greet their dog first is 0.475 to 0.775.
Calculate the point estimate for the 95% confidence interval:  _______ 
Calculate the margin of error for the 95% confidence interval: _______ 

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4

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A Gallup poll asked a random sample of U.S. adults, “Would you like to lose weight?”
Based on this poll, the 95% confidence interval for the proportion of all U.S. adults who want to lose weight is 0.56 to 0.62.
Interpret the confidence level.
I will grade this question by hand.

Required

4

Required

1

In the description of its methodology, Gallup states that the 3 percentage point margin of error for this poll includes only sampling variability (what it calls “sampling error”).
What other potential sources of error (Gallup calls these “nonsampling errors”) could affect the accuracy of the 95% confidence interval?

Hint, what does the Margin of Error not account for?
Explain how it could affect the results.
I will grade this problem.

Tim purchased a random sample of clementines at a local grocery store. The 95% confidence interval for the mean weight of all clementines at this store is 76.6 grams to 90.1 grams. Interpret this confidence interval.

We are 95% confident that the interval of 76.6 - 90.1 grams contains the true mean weight of all clementines.

95% of the clementines at this store weigh between 76.6 to 90.1 grams.

The weight of a sample of clementines will weight from 76.6 to 90.1 grams 95% of the time.

95% of the samples of clementines will weigh between 76.6 to 90.1 grams.

Calculate the point estimate and margin of error used to create the confidence interval in #1.
Point estimate = _______ 
Margin of Error = _______ 

The nutritional label on a bag of clementines says a typical clementine weighs 74 grams. Does the interval in #1 & 2 provide convincing evidence that the mean weight of clementines from this store is larger than the nutritional label suggests?
Explain.

Yes, there is convincing evidence that the mean weight of clementines from this store is larger than the nutritional label suggests,

No, there is not convincing evidence that the mean weight of clementines from this store is larger than the nutritional label suggests,

because the 95% confidence interval contains 74 grams.

because the 95% confidence interval does not contain 74 grams, 74 g. is less than the lower limit of the interval.

because the 95% confidence interval does not contain 74 grams, 74 g. is greater than the upper limit of the interval.

The Pew Research Center and Smithsonian magazine recently quizzed a random sample of 1006 U.S. adults on their knowledge of science.
One of the questions asked, “Which is the better way to determine whether a new drug is effective in treating a disease?
If a scientist has a group of 1000 volunteers with the disease to study, should she
(a) Give the drug to all of them and see how many get better or
(b) Give the drug to half of them and not to the other half, and compare how many in each group get better?”

A 95% confidence interval for the proportion of U.S. adults who would correctly answer (b) is 0.723 to 0.777.
Interpret this confidence interval. Use the sentence frame from our notes.
I will grade your answer to this question by hand.

Calculate the point estimate and margin of error used to create the confidence interval in #4.
Point estimate = _______ 
Margin of Error = _______ 

Refer to Exercise 4.
If people guess one of the two choices at random, about 50% should get the answer correct. Does the interval in Exercise 4 provide convincing evidence that more than 50% of all U.S. adults would answer this question correctly?
Explain.
Hint: change 50% to a proportion to help answer.

Yes, there is convincing evidence that more than 50% of all U.S. adults would answer this question correctly,

No, there is not convincing evidence that more than 50% of all U.S. adults would answer this question correctly,

because the 95% confidence interval contains 50%.

because the 95% confidence interval does not contain 50%, 50% is less than the lower limit of the interval.

because the 95% confidence interval does not contain 50%, 50% is greater than the upper limit of the interval.

A magazine reported that 66% of all dog owners usually greet their dog before greeting their spouse or children when they return home at the end of the workday. 
Researchers select 40 dog owners at random and ask them whom they greet first when returning home. 
The 95% confidence interval for the proportion of owners who greet their dog first is 0.475 to 0.775.
Calculate the point estimate for the 95% confidence interval:  _______ 
Calculate the margin of error for the 95% confidence interval: _______ 

Refer to Exercise 7.
Based on the confidence interval, is it plausible that the true proportion of all owners who greet their dog first is 66%? Explain.

Yes, there is convincing evidence that the true proportion of all owners who greet their dog first is 66%,

because the 95% confidence interval does not contain 66%, 66% is less than the lower limit of the interval.

because the 95% confidence interval contains 66%.

No, there is not convincing evidence that the true proportion of all owners who greet their dog first is 66%,

because the 95% confidence interval does not contain 66%, 66% is greater than the upper limit of the interval.

The puzzle editor of a game magazine asked 43 randomly selected subscribers how long it took them to complete a certain crossword puzzle.
The 99% confidence interval for the median completion time for all subscribers is 15.2 to 18.6 minutes.
Interpret the confidence level.
CAUTION: The confidence level does not tell us the probability that a particular confidence interval captures the population parameter.

We are 99% confident that the interval of 15.2 to 18.6 minutes contains the true mean completion time.

If we took many many random samples of 43 subscribers and constructed 99% confidence intervals, about 99% of them would contain the true mean completion time.

It took the crossword puzzlers 99% less time than the average person to do the crossword puzzles.

99% of the time the crossword puzzlers could complete the crossword puzzles.

Explain what would happen in the following situations.

Explain what would happen to the length of the interval if the confidence level were decreased to 90%
Explain what would happen to the length of the interval if the sample size were decreased to 15.
Explain what would happen to the length of the interval if the sample size were increased to 100.
Explain what would happen to the length of the interval if the confidence level were increased to 100%

Length of Confidence Interval would decrease
Length of Confidence Interval would increase

The puzzle editor originally sent requests for completion times to 150 subscribers, only 43 of whom reported their times.
Describe one potential source of bias in the study that is not accounted for by the margin of error.

not everyone responded to the survey.

not everyone could respond to the survey

Response Bias

Nonresponse Bias

the survey was worded in a way that will influence the response of the subjects.

Undercoverage Bias

A Gallup poll asked a random sample of U.S. adults, “Would you like to lose weight?”
Based on this poll, the 95% confidence interval for the proportion of all U.S. adults who want to lose weight is 0.56 to 0.62.
Interpret the confidence level.
I will grade this question by hand.

Match the scenario with what would happen to the confidence interval.

Explain what would happen to the length of the interval if the sample size was twice as big as in the actual study.
Explain what would happen to the length of the interval if the confidence level were increased to 99%
Explain what would happen to the length of the interval if the sample size was only half as big as in the actual study.
Explain what would happen to the length of the interval if the confidence level were decreased to 85%

Confidence Interval would increase.
Confidence interval would decrease.

In the description of its methodology, Gallup states that the 3 percentage point margin of error for this poll includes only sampling variability (what it calls “sampling error”).
What other potential sources of error (Gallup calls these “nonsampling errors”) could affect the accuracy of the 95% confidence interval?

Hint, what does the Margin of Error not account for?
Explain how it could affect the results.
I will grade this problem.

Tim purchased a random sample of clementines at a local grocery store. The 95% confidence interval for the mean weight of all clementines at this store is 76.6 grams to 90.1 grams. Interpret this confidence interval.

We are 95% confident that the interval of 76.6 - 90.1 grams contains the true mean weight of all clementines.

95% of the clementines at this store weigh between 76.6 to 90.1 grams.

The weight of a sample of clementines will weight from 76.6 to 90.1 grams 95% of the time.

95% of the samples of clementines will weigh between 76.6 to 90.1 grams.

The nutritional label on a bag of clementines says a typical clementine weighs 74 grams. Does the interval in #1 & 2 provide convincing evidence that the mean weight of clementines from this store is larger than the nutritional label suggests? 
Explain.

Yes, there is convincing evidence that the mean weight of clementines from this store is larger than the nutritional label suggests,

No, there is not convincing evidence that the mean weight of clementines from this store is larger than the nutritional label suggests,

because the 95% confidence interval contains 74 grams.

because the 95% confidence interval does not contain 74 grams, 74 g. is less than the lower limit of the interval.

because the 95% confidence interval does not contain 74 grams, 74 g. is greater than the upper limit of the interval.

Refer to Exercise 4. 
If people guess one of the two choices at random, about 50% should get the answer correct. Does the interval in Exercise 4 provide convincing evidence that more than 50% of all U.S. adults would answer this question correctly? 
Explain.
Hint: change 50% to a proportion to help answer.

Yes, there is convincing evidence that more than 50% of all U.S. adults would answer this question correctly,

No, there is not convincing evidence that more than 50% of all U.S. adults would answer this question correctly,

because the 95% confidence interval contains 50%.

because the 95% confidence interval does not contain 50%, 50% is less than the lower limit of the interval.

because the 95% confidence interval does not contain 50%, 50% is greater than the upper limit of the interval.

Refer to Exercise 7. 
Based on the confidence interval, is it plausible that the true proportion of all owners who greet their dog first is 66%? Explain.

Yes, there is convincing evidence that the true proportion of all owners who greet their dog first is 66%,

because the 95% confidence interval does not contain 66%, 66% is less than the lower limit of the interval.

because the 95% confidence interval contains 66%.

No, there is not convincing evidence that the true proportion of all owners who greet their dog first is 66%,

because the 95% confidence interval does not contain 66%, 66% is greater than the upper limit of the interval.

The puzzle editor of a game magazine asked 43 randomly selected subscribers how long it took them to complete a certain crossword puzzle. 
The 99% confidence interval for the median completion time for all subscribers is 15.2 to 18.6 minutes. 
Interpret the confidence level.
CAUTION: The confidence level does not tell us the probability that a particular confidence interval captures the population parameter.

We are 99% confident that the interval of 15.2 to 18.6 minutes contains the true mean completion time.

If we took many many random samples of 43 subscribers and constructed 99% confidence intervals, about 99% of them would contain the true mean completion time.

It took the crossword puzzlers 99% less time than the average person to do the crossword puzzles.

99% of the time the crossword puzzlers could complete the crossword puzzles.

Explain what would happen in the following situations.

Explain what would happen to the length of the interval if the confidence level were decreased to 90%

Explain what would happen to the length of the interval if the sample size were decreased to 15.

Explain what would happen to the length of the interval if the sample size were increased to 100.

Explain what would happen to the length of the interval if the confidence level were increased to 100%

Length of Confidence Interval would decrease

Length of Confidence Interval would increase

The puzzle editor originally sent requests for completion times to 150 subscribers, only 43 of whom reported their times. 
Describe one potential source of bias in the study that is not accounted for by the margin of error.

not everyone responded to the survey.

not everyone could respond to the survey

Response Bias

Nonresponse Bias

the survey was worded in a way that will influence the response of the subjects.

Undercoverage Bias

Match the scenario with what would happen to the confidence interval.

Explain what would happen to the length of the interval if the sample size was twice as big as in the actual study.

Explain what would happen to the length of the interval if the confidence level were increased to 99%

Explain what would happen to the length of the interval if the sample size was only half as big as in the actual study.

Explain what would happen to the length of the interval if the confidence level were decreased to 85%

Confidence Interval would increase.

Confidence interval would decrease.

Lessons 7.1 & 7.2 Partner Content Check

Lessons 7.1 & 7.2 Partner Content Check

A Gallup poll asked a random sample of U.S. adults, “Would you like to lose weight?” Based on this poll, the 95% confidence interval for the proportion of all U.S. adults who want to lose weight is 0.56 to 0.62. Interpret the confidence level.I will grade this question by hand.

Tim purchased a random sample of clementines at a local grocery store. The 95% confidence interval for the mean weight of all clementines at this store is 76.6 grams to 90.1 grams. Interpret this confidence interval.

The nutritional label on a bag of clementines says a typical clementine weighs 74 grams. Does the interval in #1 & 2 provide convincing evidence that the mean weight of clementines from this store is larger than the nutritional label suggests? Explain.

Refer to Exercise 7. Based on the confidence interval, is it plausible that the true proportion of all owners who greet their dog first is 66%? Explain.

Explain what would happen in the following situations.

The puzzle editor originally sent requests for completion times to 150 subscribers, only 43 of whom reported their times. Describe one potential source of bias in the study that is not accounted for by the margin of error.

A Gallup poll asked a random sample of U.S. adults, “Would you like to lose weight?” Based on this poll, the 95% confidence interval for the proportion of all U.S. adults who want to lose weight is 0.56 to 0.62. Interpret the confidence level.I will grade this question by hand.

Match the scenario with what would happen to the confidence interval.

A Gallup poll asked a random sample of U.S. adults, “Would you like to lose weight?”
Based on this poll, the 95% confidence interval for the proportion of all U.S. adults who want to lose weight is 0.56 to 0.62.
Interpret the confidence level.
I will grade this question by hand.

The nutritional label on a bag of clementines says a typical clementine weighs 74 grams. Does the interval in #1 & 2 provide convincing evidence that the mean weight of clementines from this store is larger than the nutritional label suggests?
Explain.

Refer to Exercise 7.
Based on the confidence interval, is it plausible that the true proportion of all owners who greet their dog first is 66%? Explain.

The puzzle editor originally sent requests for completion times to 150 subscribers, only 43 of whom reported their times.
Describe one potential source of bias in the study that is not accounted for by the margin of error.

A Gallup poll asked a random sample of U.S. adults, “Would you like to lose weight?”
Based on this poll, the 95% confidence interval for the proportion of all U.S. adults who want to lose weight is 0.56 to 0.62.
Interpret the confidence level.
I will grade this question by hand.