Deck 8: Nutrition

Question 1

A random sample of 30 business students required an average of 43.4 minutes to complete a statistics exam. Assume that the population standard deviation to complete the exam was 8.7 minutes. The margin of error for a 98% confidence interval around this sample mean is ------.

A)3.12
B)3.70
C)2.04
D)2.62

Answer 1

3.70

Question 2

"Gamers" are described as people who regularly play video games. A random sample of 80 people was selected and 50 were found to be male. The 90% confidence interval for the proportion based on this sample is ________ .

A)(0.463, 0.787)
B)(0.598, 0.652)
C)(0.571, 0.679)
D)(0.536, 0.714)

Answer 2

(0.536, 0.714)

Question 3

A statistics professor has 115 students in a statistics class and would like to estimate the number of hours each student studied for the last exam. A random sample of 41 students was found to study an average of 7.3 hours with a standard deviation of 1.9 hours. The 98% confidence interval to estimate the average number of hours studying for the exam is _____.

A)(6.72, 7.88)
B)(5.18, 9.42)
C)(5.82, 8.79)
D)(6.11, 8.49)

Answer 3

(6.72, 7.88)

Question 4

The critical value for an 84% confidence interval for the proportion is ---------.

A)± 1.41
B)± 2.65
C)± 1.00
D)± 1.96

Question 5

The Retail Advertising and Marketing Association would like to estimate the average amount of money that a person spends for Mother's Day with a 99% confidence interval and a margin of error within plus or minus $6. Assuming the standard deviation for spending on Mother's Day is $36, the required sample size is _________.

A)284
B)239
C)313
D)210

Question 6

The --------- represents the probability that any given confidence interval will not contain the true population mean.

A)significance level
B)margin of error
C)confidence level
D)confidence interval

Question 7

Verizon Wireless would like to estimate the proportion of households that use cell phones for their phone service without a land line. A random sample of 150 households was selected and 48 relied strictly on cell phones for their service. The approximate standard error of the proportion for this sample is _______.

A)0.0381
B)0.0419
C)0.0580
D)0.0225

Question 8

A _________ is defined as the probability that the interval estimate will include the population parameter of interest, such as a mean or a proportion.

A)confidence level
B)significance level
C)margin of error
D)confidence interval

Question 9

A random sample of 150 mortgages in the state of Mississippi was randomly selected. From this sample, 17 were found to be delinquent on their current payment. Using this sample, the point estimate for the proportion of delinquent mortgages in Mississippi is _________.

A)0.102
B)0.113
C)0.080
D)0.137

Question 10

A random sample of 150 mortgages in the state of Mississippi was randomly selected. From this sample, 17 were found to be delinquent on their current payment. The margin of error for an 80% confidence interval for the proportion based on this sample is __________.

A)0.0695
B)0.0522
C)0.0330
D)0.0258

Question 11

When calculating a confidence interval for the mean using a sample size of 30 or more with a known population standard deviation, the _______ is used.

A)Poisson distribution
B)normal distribution
C)Student's t-distribution
D)binomial distribution

Question 12

A random sample of 35 business students required an average of 50.7 minutes to complete a statistics exam. Assume that the population standard deviation to complete the exam was 10.4 minutes. The 95% confidence interval around this sample mean is ________.

A)(48.9, 52.5)
B)(47.3, 54.1)
C)(49.8, 51.6)
D)(45.4, 56.0)

Question 13

Dr. Jordan operates a dental practice with 315 patients and she would like to estimate the proportion of her patients that have dental insurance from their employers. A random sample of 110 patients found that 40 had insurance coverage. The 95% confidence interval to estimate the proportion of patients with dental insurance is _____________.

A)(0.346, 0.383)
B)(0.327, 0.401)
C)(0.227, 0.501)
D)(0.291, 0.437)

Question 14

The average natural gas bill for a random sample of 26 homes in the 19808 zip code during the month of March was $305.30 with a sample standard deviation of $46.50. The 80% confidence interval around this sample mean is ______ .

A)($293.30, $317.30)
B)($268.82, $341.78)
C)($277.94, $332.66)
D)($287.06, $323.54)

Question 15

The National Center for Education would like to estimate the proportion of students who defaulted on their student loans for the state of Arizona. A pilot sample of 50 students with loans from Arizona found that eight had defaulted on their loans. The total sample size needed to construct a 95% confidence interval for the proportion of student loans in default with a margin of error equal to 4% is _____ .

A)389
B)410
C)365
D)323

Question 16

A local church has a congregation consisting of 480 adult members. The church's administrators would like to estimate the average weekly donation per member per week. A random sample of 65 members was found to have an average donation of $50.40 and a standard deviation of $12.30. The 95% confidence interval to estimate the average weekly donation is _______ .

A)($44.30, $56.08)
B)($43.30, $57.50)
C)($45.41, $55.39)
D)($47.56, $53.24)

Question 17

Increasing the sample size when calculating a confidence interval while keeping the confidence level constant will

A)increase the margin of error resulting in a narrower (more precise)confidence interval.
B)reduce the margin of error resulting in a narrower (more precise)confidence interval.
C)reduce the margin of error resulting in a wider (less precise)confidence interval.
D)increase the margin of error resulting in a wider (more precise)confidence interval.

Question 18

A _______ is a single value that best describes the population of interest.

A)confidence level
B)confidence interval
C)margin of error
D)point estimate

Question 19

The federal government would like to estimate the proportion of families with no savings. A pilot sample of 60 families found that 18 had no savings. The total sample size needed to construct a 95% confidence interval for the proportion of families with no savings with a margin of error equal to 6% is_________ .

A)225
B)425
C)397
D)460

Question 20

The average natural gas bill for a random sample of 26 homes in the 19808 zip code during the month of March was $305.30 with a sample standard deviation of $46.50. The critical value for a 95% confidence interval around this sample mean is __________ .

A)1.706
B)1.708
C)2.056
D)2.060

Question 21

A random sample of 25 roundtrip flights between Philadelphia and Dallas has an average airfare of $393.50 with a sample standard deviation of $50.30. The critical value for an 80% confidence interval around this sample mean is ------.

A)1.318
B)0.857
C)1.711
D)2.064

Question 22

A random sample of 13 hotels in Boston had an average nightly room rate of $172.10 with a sample standard deviation of $23.90. The approximate standard error of the mean for this sample is --------.

A)6.62
B)14.16
C)13.84
D)11.56

Question 23

Steve's average golf score at his local course is 93.6 from a random sample of 34 rounds of golf. Assume that the population standard deviation for his golf score is 4.2. The 90% confidence interval around this sample mean is ------.

A)(90.5, 96.7)
B)(89.0, 98.3)
C)(92.4, 94.8)
D)(93.2, 94.0)

Question 24

John Charleston owns a heating oil delivery company that services 1,540 residences. John would like to estimate the number of customers that have oil storage tanks that are less than 100 gallons in capacity. A random sample of 200 customers found that 48 had an oil tank that was less than 100 gallons. The 99% confidence interval to estimate the proportion of customers with oil tanks less than 100 gallons is ------.

A)(0.212, 0.268)
B)(0.167, 0.313)
C)(0.184, 0.296)
D)(0.225, 0.255)

Question 25

A random sample of 150 mortgages in the state of Mississippi was randomly selected. From this sample, 17 were found to be delinquent on their current payment. The approximate standard error of the proportion for this sample is -------.

A)0.0406
B)0.0145
C)0.0567
D)0.0258

Question 26

A local church has a congregation consisting of 480 adult members. The church's administrators would like to estimate the average weekly donation per member per week. A random sample of 90 members was found to have an average donation of $56.70 and a standard deviation of $10.50. The 90% confidence interval to estimate the average weekly donation is ______ .

A)($44.71, $68.69)
B)($55.04, $58.36)
C)($49.93, $63.48)
D)($46.73, $66.67)

Question 27

When calculating a confidence interval for the mean using a sample size of less than 30 with an unknown population standard deviation, the ------- is used.

A)binomial distribution
B)normal distribution
C)Poisson distribution
D)Student's t-distribution

Question 28

Verizon Wireless would like to estimate the proportion of households that use cell phones for their phone service without a land line. A random sample of 150 households was selected and 48 relied strictly on cell phones for their service. The margin of error for a 90% confidence interval for the proportion based on this sample is ------.

A)0.0561
B)0.0627
C)0.0333
D)0.0475

Question 29

A random sample of 13 hotels in Boston had an average nightly room rate of $172.10 with a sample standard deviation of $23.90. The 99% confidence interval around this sample mean is -------- .

A)($165.48, $178.72)
B)($155.55, $188.65)
C)($158.86, $185.34)
D)($151.88, $192.32)

Question 30

A random sample of 25 roundtrip flights between Philadelphia and Dallas has an average airfare of $393.50 with a sample standard deviation of $50.30. The margin of error for a 90% confidence interval around this sample mean is -----.

A)22.9
B)14.1
C)10.6
D)17.2

Question 31

Steve's average golf score at his local course is 92.9 from a random sample of 60 rounds of golf. Assume that the population standard deviation for his golf score is 4.2. The standard error of the mean for this sample is ---------- .

A)1.17
B)1.56
C)2.30
D)0.54

Question 32

A random sample of 16 roundtrip flights between Philadelphia and Dallas has an average airfare of $422.10 with a sample standard deviation of $56.30. The approximate standard error of the mean for this sample is --------.

A)$20.32
B)$24.19
C)$10.11
D)$14.08

Question 33

A random sample of 16 roundtrip flights between Philadelphia and Dallas has an average airfare of $422.10 with a sample standard deviation of $56.30. The 98% confidence interval around this sample mean is --------.

A)($385.48, $458.72)
B)($415.06, $429.14)
C)($400.99, $443.21)
D)($365.80, $478.40)

Question 34

The National Center for Education would like to estimate the proportion of students who defaulted on their student loans for the state of Arizona. The total sample size needed to construct a 95% confidence interval for the proportion of student loans in default with a margin of error equal to 4% is -------.

A)336
B)601
C)416
D)455

Question 35

A random sample of 25 roundtrip flights between Philadelphia and Dallas has an average airfare of $393.50 with a sample standard deviation of $50.30. The 95% confidence interval around this sample mean is ------ .

A)($353.26, $433.74)
B)($388.47, $398.53)
C)($383.44, $403.56)
D)($372.74, $414.26)

Question 36

The Girl Scouts would like to estimate the proportion of people who consider Thin Mints to be their favorite Girl Scout cookie. A pilot sample of 60 cookie customers found that 15 favored Thin Mint cookies. The total sample size needed to construct a 90% confidence interval for the proportion of customers who favor Thin Mint cookies with a margin of error equal to 6% is ----.

A)141
B)270
C)235
D)187

Question 37

A random sample of 17 hotels in Boston had an average nightly room rate of $165.40 with a sample standard deviation of $21.70. The critical value for a 98% confidence interval around this sample mean is -------.

A)2.583
B)2.898
C)2.567
D)2.921

Question 38

The U.S. Census Bureau would like to estimate the average square footage of a new single-family home with a 95% confidence interval and a margin of error within plus or minus 100 square feet. Assuming the standard deviation for the square footage of new single-family homes is 850 square feet, the required sample size is ----------.

A)203
B)278
C)232
D)295

Question 39

A ________ for the mean is an interval estimate around a sample mean that provides us with a range of where the true population mean lies.

A)confidence interval
B)margin of error
C)significance level
D)confidence level

Question 40

The U.S. Census Bureau would like to estimate the average square footage of a new single-family home with a 95% confidence interval and a margin of error within plus or minus 200 square feet. Assuming the standard deviation for the square footage of new single-family homes is 850 square feet, the required sample size is ---------.

A)70
B)48
C)55
D)41

Question 41

The average natural gas bill for a random sample of 21 homes in the 19808 zip code during the month of March was $311.90 with a sample standard deviation of $51.60. The 90% confidence interval around this sample mean is ------.

A)($266.82, $356.98)
B)($292.46, $331.34)
C)($278.09, $345.71)
D)($285.98, $337.82)

Question 42

Verizon Wireless would like to estimate the proportion of households that use cell phones for their phone service without a land line. A random sample of 150 households was selected and 48 relied strictly on cell phones for their service. Using this sample, the point estimate for the proportion of households without land lines is ------------.

A)0.32
B)0.25
C)0.48
D)0.53

Question 43

According to the Entertainment Software Association, the average age of "gamers" (those that routinely play video games)is 30 years old. A random sample of 33 gamers people had an average age of 32.7 years old. Assume that the population standard deviation for the age of gamers is 4.6 years. Use a 90% confidence interval to test the validity of this report and choose the one statement that is correct.

A)Because this confidence interval does not include 30 years, the report by the Entertainment Software Association is not validated.
B)Because this confidence interval does include 30 years, the report by the Entertainment Software Association is not validated.
C)Because this confidence interval does not include 30 years, the report by the Entertainment Software Association is validated.
D)Because this confidence interval does include 30 years, the report by the Entertainment Software Association is validated.

Question 44

"Gamers" are described as people who regularly play video games. A random sample of 80 people was selected and 50 were found to be male. The approximate standard error of the proportion for this sample is ________ .

A)0.0422
B)0.0610
C)0.0541
D)0.0336

Question 45

Which one of the following statements is not true regarding the characteristics of the Student's t-d istribution?

A)The area under the curve is equal to 1.0.
B)The shape of the Student's t-distribution is narrower than the shape of the normal distribution.
C)As the number of degrees of freedom increases, the shape of the Student's t-distribution becomes similar to the normal distribution.
D)It is bell-shaped and symmetrical around the mean of the distribution.

Question 46

When calculating a confidence interval for proportions, we assume that proportion data follow the

A)binomial distribution.
B)Student's t-distribution.
C)uniform distribution.
D)Poisson distribution.

Question 47

A statistics professor has 115 students in a statistics class and would like to estimate the number of hours each student studied for the last exam. A random sample of 24 students was found to study an average of 6.8 hours with a standard deviation of 2.2 hours. The 90% confidence interval to estimate the average number of hours studying for the exam is ________.

A)(5.79, 7.81)
B)(5.86, 8.74)
C)(6.69, 6.91)
D)(6.11, 7.49)

Question 48

A survey by American Express Spending reported that the average amount spent on a wedding gift for a close family member is $166. A random sample of 45 people who purchased wedding gifts for a close family member spent an average of $160.50. Assume that the population standard deviation is $38. Use a 95% confidence interval to test the validity of this report and choose the one statement that is correct.

A)Because this confidence interval does not include $166, the report by American Express Spending is not validated.
B)Because this confidence interval does include $166, the report by American Express Spending is not validated.
C)Because this confidence interval does include $166, the report by American Express Spending is validated.
D)Because this confidence interval does not include $166, the report by American Express Spending is validated.

Question 49

"Gamers" are described as people who regularly play video games. A random sample of 120 people was selected and 66 were found to be male. Using this sample, the point estimate for the proportion of gamers who are male is ________ .

A)0.55
B)0.71
C)0.75
D)0.66

Question 50

The National Center for Education would like to estimate the average student debt for the state of Ohio with a 90% confidence interval and a margin of error within plus or minus $1,800. Assuming the standard deviation for student debt in this state is $7,500, the required sample size is _________ .

A)47
B)80
C)36
D)65

Question 51

The average natural gas bill for a random sample of 21 homes in the 19808 zip code during the month of March was $311.90 with a sample standard deviation of $51.60. The approximate standard error of the mean for this sample is _____ .

A)8.20
B)14.74
C)9.93
D)11.27

Question 52

A random sample of 60 business students required an average of 50.7 minutes to complete a statistics exam. Assume that the population standard deviation to complete the exam was 10.4 minutes. The 98% confidence interval around this sample mean is____ .

A)(47.6, 53.8)
B)(45.4, 56.0)
C)(49.8, 51.6)
D)(48.9, 52.5)

Question 53

The Girl Scouts would like to estimate the proportion of people who consider Thin Mints to be their favorite Girl Scout cookie. The total sample size needed to construct a 90% confidence interval for the proportion of customers who favor Thin Mint cookies with a margin of error equal to 6% is .

A)145
B)247
C)188
D)285

Question 54

The National Center for Education would like to estimate the average student debt for the state of Ohio with a 95% confidence interval and a margin of error within plus or minus $2,500. Assuming the standard deviation for student debt in this state is $8,000, the required sample size is _______.

A)62
B)40
C)78
D)95

Question 55

A______ confidence interval might be most appropriate during the early stages of a research project when little is known about the population's parameters and the project's researchers might still be gauging the parameters.

A)100%
B)95%
C)99%
D)90%

Question 56

Dr. Jordan operates a dental practice with 315 patients and she would like to estimate the proportion of her patients that have dental insurance from their employers. A random sample of 75 patients found that 30 had insurance coverage. The 90% confidence interval to estimate the proportion of patients with dental insurance is _______.

A)(0.252, 0.548)
B)(0.319, 0.481)
C)(0.276, 0.524)
D)(0.202, 0.598)

Question 57

The Retail Advertising and Marketing Association would like to estimate the average amount of money that a person spends for Mother's Day with a 99% confidence interval and a margin of error within plus or minus $12. Assuming the standard deviation for spending on Mother's Day is $36, the required sample size is _________.

A)60
B)72
C)108
D)97

Question 58

A _______ confidence interval is often used in scientific or medical research when making a wrong conclusion about a population parameter is very costly.

A)95%
B)99%
C)90%
D)100%

Question 59

A random sample of 150 mortgages in the state of Mississippi was randomly selected. From this sample, 17 were found to be delinquent on their current payment. The 98% confidence interval for the proportion based on this sample is ______.

A)(0.103, 0.216)
B)(0.074, 0.152)
C)(0.053, 0.173)
D)(0.095, 0.131)

Question 60

The average natural gas bill for a random sample of 26 homes in the 19808 zip code during the month of March was $305.30 with a sample standard deviation of $46.50. The margin of error for a 98% confidence interval around this sample mean is -----.

A)$25.20
B)$22.66
C)$18.69
D)$20.15

Question 61

The federal government would like to estimate the proportion of families with no savings. The total sample size needed to construct a 95% confidence interval for the proportion of families with no savings with a margin of error equal to 6% is __________.

A)318
B)480
C)277
D)138

Question 62

If a pilot sample is not available, it is recommended to set the sample proportion equal to 0.50 to calculate the required sample size for a confidence interval for the proportion.

Question 63

The point estimate may not equal the true population mean because of the presence of sampling error.

Question 64

The critical z-score for a 98% confidence level is ________.

A)2.575
B)1.28
C)2.33
D)1.96

Question 65

Verizon Wireless would like to estimate the proportion of households that use cell phones for their phone service without a land line. A random sample of 150 households was selected and 48 relied strictly on cell phones for their service. The 95% confidence interval for the proportion based on this sample is ------- .

A)(0.257, 0.383)
B)(0.185, 0.456)
C)(0.223, 0.417)
D)(0.165, 0.475)

Question 66

Steve's average golf score at his local course is 93.6 from a random sample of 34 rounds of golf. Assume that the population standard deviation for his golf score is 4.2. The margin of error for a 95% confidence interval around this sample mean is---------- .

A)1.41
B)1.18
C)1.68
D)0.92

Question 67

When we use the t-distribution to calculate a confidence interval, we need to assume that the population of interest follows the normal probability distribution.

Question 68

The purpose of generating a confidence interval for the mean is to provide an estimate for the value of the population mean.

Question 69

John Charleston owns a heating oil delivery company that services 1,540 residences. John would like to estimate the number of customers that have oil storage tanks that are less than 100 gallons in capacity. A random sample of 200 customers found that 63 had an oil tank that was less than 100 gallons. The 80% confidence interval to estimate the proportion of customers with oil tanks less than 100 gallons is______ .

A)(0.151, 0.480)
B)(0.183, 0.447)
C)(0.276, 0.354)
D)(0.216, 0.414)

Question 70

The margin of error for a sample is dependent on the sample mean.

Question 71

A __________ represents the width of the confidence interval between a sample mean and its upper limit or between a sample mean and its lower limit.

A)confidence level
B)significance level
C)confidence interval
D)margin of error

Question 72

A 100% confidence interval is more accurate than a 90% confidence interval and is therefore more preferable.

Question 73

The confidence interval for the mean is symmetrical around the population mean.

Question 74

The ------ confidence interval is a "workhorse" in the field of statistics and is seen far more than any other confidence level.

A)99%
B)95%
C)90%
D)100%

Question 75

A random sample of 17 hotels in Boston had an average nightly room rate of $165.40 with a sample standard deviation of $21.70. The 90% confidence interval around this sample mean is___ .

A)($144.32, $186.32)
B)($162.76, $168.04)
C)($152.22, $178.58)
D)($156.20, $174.60)

Question 76

The shape of the t-distribution becomes similar to the binomial distribution as the sample size increases.

Question 77

Steve's average golf score at his local course is 92.9 from a random sample of 60 rounds of golf. Assume that the population standard deviation for his golf score is 4.2. The 99% confidence interval around this sample mean is ----- .

A)(90.7, 95.1)
B)(89.5, 96.3)
C)(87.6, 98.2)
D)(92.4, 94.2)

Question 78

A sample proportion equal to 0.50 will require the smallest sample size to achieve a particular margin of error for a confidence interval for the proportion.

Question 79

"Gamers" are described as people who regularly play video games. A random sample of 80 people was selected and 50 were found to be male. The margin of error for a 95% confidence interval for the proportion based on this sample is -----------.

A)0.0618
B)0.0756
C)0.1060
D)0.0527

Question 80

The degrees of freedom are used to determine the critical z-score for the normal distribution when calculating a confidence interval.