Question 1

How tall is your average statistics classmate? To determine this,you measure the height of a random sample of 15 of your 100 fellow students,finding a 95% confidence interval for the mean height of 164.76 to 170.90 cm.

Accepted Answer

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Question 2

How many unpopped kernels are left when you pop a bag of microwave popcorn? Quality control personnel at Yummy Popcorn take a random sample of 50 bags of popcorn.They pop each bag in a microwave and then count the number of unpopped kernels.The following interval is produced:
T-interval for μ : with 99% Confidence,11 < μ(unpopped)< 25

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Question 3

A researcher wants to estimate the mean cholesterol level of people in his city.A random sample of 21 people yields an average cholesterol level of 219,with a margin of error of ±12.Assume the researcher used a confidence level of 90%.

Accepted Answer

The margin of error (±12) reflects the accuracy of the estimate and corresponds to the t*d/SQRT(n) formula, where t is the critical value for the 90% confidence level and S is the sample standard deviation (which is unknown). Therefore, we can calculate that t*d/SQRT(n) = 12 leads to a range of 207 to 231 for the mean cholesterol level in the population with 90% confidence. This means that we can be 90% confident that the true mean cholesterol level of people in the city is in this interval. None of the other choices accurately reflects this interpretation.

Question 4

Alarmed at the rising gas prices in your town,you decide to estimate the average gas price for a litre of regular unleaded gasoline.From your sample of 25 gas stations,you calculate a 90% confidence interval of ($1.33,$1.41)

Accepted Answer

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Question 5

A random sample of clients at a weight loss centre were given a dietary supplement to see if it would promote weight loss.The centre reported that the 20 clients lost an average of 15.3 kg,and that a 95% confidence interval for the mean weight loss this supplement produced has a margin of error of ±4.5 kg.

Accepted Answer

A 95% confidence interval means that we are 95% confident that the true population mean falls within the interval. Therefore, statement C accurately reflects this concept by stating that we are "95% confident that the mean weight loss produced by the supplement in weight loss centre clients is between 10.8 and 19.8 kg." Statement A only applies to the specific sample of 20 clients in the study, not the entire population, and statement B is too broad and unsupported without further information. Statement D uses the word "sure" which is not appropriate in statistical inference, and statement E is also too broad and only applies to future clients who may use the supplement.

Question 6

A random sample of 30 households was selected from a particular neighborhood.The number of cars for each household is shown below.Estimate the mean number of cars per household for the population of households in this neighborhood.Give the 95% confidence interval.

Accepted Answer

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Question 7

A random sample of 30 long distance runners aged 20-25 was selected from a running club.The resting heart rates (in beats per minute)of the runners are shown below.Estimate the mean resting heart rate for the population of long distance runners aged 20-25.Give the 95% confidence interval.

Accepted Answer

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Question 8

A credit union took a random sample of 40 accounts and obtained the following 90% confidence interval for the mean checking account balance at the institution: $2,193 < μ(balance)< $3,828.

Accepted Answer

The given confidence interval is only applicable to the sample of 40 accounts taken by the credit union. Therefore, option A and B are incorrect as they generalize to the entire population of the U.S. Additionally, option C is also incorrect as it suggests that the same confidence interval will be obtained for different random samples of checking accounts at the same credit union. Option E is incorrect as it misinterprets the confidence interval as a statement about the mean balance in the sample, when it is actually a statement about the true population mean balance. The correct choice is D because it correctly states that we are 90% confident that the true mean checking account balance at this credit union falls within the given interval, based on the sample of 40 accounts.

Question 9

A scientist in Smallville tested the cholesterol of a random sample of 35 town residents.He constructed the following confidence interval:
T-interval for μ: with 99.00% Confidence,188 < μ(Cholesterol)< 206

Accepted Answer

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Question 10

How much fat do reduced fat cookies typically have? You take a random sample of 51 reduced-fat cookies and test them in a lab,constructing the following confidence interval:
T-Interval for μ: with 90.00% Confidence,2.3 < μ(grams of fat)< 3.4

Accepted Answer

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Question 11

How tall is the average student on your campus? To determine this,you measure the height,in centimetres,of a random sample of 9 of your fellow 100 students and calculate the following confidence interval with 95% confidence:
155.72 < μ(height)< 181.20

Accepted Answer

The confidence interval with 95% confidence indicates that we can be 95% sure that the true population mean height of all 100 students at the campus is between 155.72 and 181.20 cm. Option B accurately represents this interpretation. Option A implies that we know the average height of all students, which is not necessarily true based on the sample data. Option C implies a probability, which is incorrect for a confidence interval. Option D is not supported by the given information, as we do not have the height of all 100 students. Option E suggests that this confidence interval is only for statistics students, which is not specified in the question.

Question 12

Based on a sample of 32 randomly selected years,a 90% confidence interval for the mean annual precipitation in one city is from 119.1 cm to 125.9 cm

Accepted Answer

Since the confidence interval is given as (119.1, 125.9), we know that the margin of error is half the width of the interval, which is (125.9 - 119.1) / 2 = 3.4. Therefore, the best choice is C) 3.4 cm.

Question 13

Based on a sample of size 42,a 95% confidence interval for the mean score of all students on an aptitude test is from 57.2 to 64.8.

Accepted Answer

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Question 14

You are considering moving to Richmond Hill,and are concerned about the average one-way commute time to downtown Toronto.Does the average one-way commute time exceed 25 minutes? You take a random sample of 50 Richmond Hill residents and find an average commute time of 29 minutes with a standard deviation of 7 minutes.

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Question 15

To determine the mean number of unpopped kernels in your favorite brand of microwave popcorn,you pop a random sample of 50 bags of popcorn and construct of 98% confidence interval of (12.5,15.4).

Accepted Answer

The answer of To determine the mean number of unpopped...

Question 16

You want to estimate the average gas price in your city for a litre of regular unleaded gasoline.From your sample of 15 gas stations,you calculate a 95% confidence interval of ($1.34,$1.40)

Accepted Answer

The 95% confidence interval means that if we were to repeat this study over and over again, 95% of the time, the true average gas price in the city would fall within the range of $1.34 to $1.40. It does not guarantee that the true average is within this range, but rather provides a range within which it is likely to fall. Therefore, option A is the best choice. Option B is incorrect as it refers to the country instead of the city. Option C is incorrect as it talks about many samples, whereas we are concerned with only a single sample here. Option D is incorrect as it refers only to the sample and not the entire population. Option E is incorrect as it makes a similar mistake as option C by talking about multiple samples.

Question 17

How much fat do reduced fat cookies typically have? You take a random sample of 51 reduced-fat cookies and test them in a lab,finding a mean fat content of 4.2 grams.You calculate a 95% confidence interval and find that the margin of error is ±0.8 grams.

Accepted Answer

The confidence interval gives the range of values within which the true population mean is likely to fall. The margin of error of ±0.8 grams means that we are 95% confident that the true population mean falls between 4.2 - 0.8 = 3.4 grams and 4.2 + 0.8 = 5 grams.

Question 18

Analysis of a random sample of 250 Nova Scotia nurses produced a 95% confidence interval for the mean annual salary of $42,807 < μ(Nurse Salary)< $49,699.

Accepted Answer

The 95% confidence interval is constructed with the intention of estimating the true mean salary of all Nova Scotia nurses with a level of confidence of 95%. Therefore, option D correctly summarizes the interpretation of the confidence interval as it acknowledges that it is an estimate for the mean salary of all nurses in Nova Scotia, and that there is a 95% chance that the true mean salary falls within this interval. Option A and C are incorrect as they suggest that the confidence interval encompasses 95% of the observed sample values, rather than the true mean salary. Option B is incorrect as it presupposes that the estimate is representative of all nurses in Canada, rather than just Nova Scotia. Option E is incorrect as it refers to the variability in confidence intervals if many random samples were taken, rather than the correct interpretation of the current confidence interval obtained from the current sample.

Question 19

Data collected by child development scientists produced the following 90% confidence interval for the average age (in months)at which children say their first word: 10.6 < μ(age)< 13.1.

Accepted Answer

This is the correct option as it accurately represents the meaning of a confidence interval. It states that based on this sample, we can estimate with 90% confidence that the true population mean (age at which children say their first word) falls between the interval of 10.6 and 13.1 months. The other options have either inaccurate or incomplete statements.

Question 20

You want to see if the number of minutes cell phone users use each month has changed from its mean of 120 minutes 2 years ago.You take a random sample of 100 cell phone users and find an average of 135 minutes used.

Accepted Answer

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Quiz 22: Inferences About Means

How tall is your average statistics classmate? To determine this,you measure the height of a random sample of 15 of your 100 fellow students,finding a 95% confidence interval for the mean height of 164.76 to 170.90 cm.

A researcher wants to estimate the mean cholesterol level of people in his city.A random sample of 21 people yields an average cholesterol level of 219,with a margin of error of ±12.Assume the researcher used a confidence level of 90%.

Alarmed at the rising gas prices in your town,you decide to estimate the average gas price for a litre of regular unleaded gasoline.From your sample of 25 gas stations,you calculate a 90% confidence interval of ($1.33,$1.41)

A random sample of 30 households was selected from a particular neighborhood.The number of cars for each household is shown below.Estimate the mean number of cars per household for the population of households in this neighborhood.Give the 95% confidence interval.

A random sample of 30 long distance runners aged 20-25 was selected from a running club.The resting heart rates (in beats per minute) of the runners are shown below.Estimate the mean resting heart rate for the population of long distance runners aged 20-25.Give the 95% confidence interval.

A credit union took a random sample of 40 accounts and obtained the following 90% confidence interval for the mean checking account balance at the institution: $2,193 < μ(balance) < $3,828.

A scientist in Smallville tested the cholesterol of a random sample of 35 town residents.He constructed the following confidence interval: T-interval for μ: with 99.00% Confidence,188 < μ(Cholesterol) < 206

How much fat do reduced fat cookies typically have? You take a random sample of 51 reduced-fat cookies and test them in a lab,constructing the following confidence interval: T-Interval for μ: with 90.00% Confidence,2.3 < μ(grams of fat) < 3.4

How tall is the average student on your campus? To determine this,you measure the height,in centimetres,of a random sample of 9 of your fellow 100 students and calculate the following confidence interval with 95% confidence: 155.72 < μ(height) < 181.20

Based on a sample of 32 randomly selected years,a 90% confidence interval for the mean annual precipitation in one city is from 119.1 cm to 125.9 cm

Based on a sample of size 42,a 95% confidence interval for the mean score of all students on an aptitude test is from 57.2 to 64.8.

To determine the mean number of unpopped kernels in your favorite brand of microwave popcorn,you pop a random sample of 50 bags of popcorn and construct of 98% confidence interval of (12.5,15.4) .

You want to estimate the average gas price in your city for a litre of regular unleaded gasoline.From your sample of 15 gas stations,you calculate a 95% confidence interval of ($1.34,$1.40)

How much fat do reduced fat cookies typically have? You take a random sample of 51 reduced-fat cookies and test them in a lab,finding a mean fat content of 4.2 grams.You calculate a 95% confidence interval and find that the margin of error is ±0.8 grams.

Analysis of a random sample of 250 Nova Scotia nurses produced a 95% confidence interval for the mean annual salary of $42,807 < μ(Nurse Salary) < $49,699.

Data collected by child development scientists produced the following 90% confidence interval for the average age (in months) at which children say their first word: 10.6 < μ(age) < 13.1.

You want to see if the number of minutes cell phone users use each month has changed from its mean of 120 minutes 2 years ago.You take a random sample of 100 cell phone users and find an average of 135 minutes used.