qmb quiz 3

Recently, 18.3% of visitors to the Travelocity website hailed from the Google search engine. A random sample of 130 visitors on the Travelocity website was selected. The standard error of the proportion is ________.

0.0339

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 ________.

0.0381

According to IDC, Apple's share of the smartphone market was 40% during a recent quarter. A random sample of 90 smartphone users was selected. The standard error of the proportion is ________.

0.0516

Recent survey data indicated that 14.2% of adults between the ages of 25 and 34 live with their parents. Their parents must have a basement! A random sample of 125 young adults in this age group was selected. What is the probability that between 13 and 17 of these young adults lived with their parents? Hint: use 14.2% to determine the standard error and the p-bar would be the 13/125 and the 17/125.

0.3120

Scotland has been a member of the United Kingdom since the 1707 Act of Union. In a recent poll, 38% of Scots would vote in favor of leaving the U.K. A random sample of 135 Scots was selected. What is the probability that between 50 and 60 of them were in favor of leaving the U.K.?

0.5297

A recent study reported that 28% of shoppers only review one page when searching online for product information. A random sample of 100 shoppers was randomly selected. What is the probability that between 20 and 30 of these shoppers only review one page when searching online?

0.6346

The Wall Street Journal reported that a recently conducted travel found that 28% of baby boomers (those born between 1946 and 1964) took a cruise vacation within the last three years. A random sample of 75 baby boomers was selected. What is the probability that 23 or fewer of these individuals took a cruise within the last three years? Hint: use the 28% to determine the standard error and the 23/75 as the p-bar.

0.6965

A recent study reported that 73% of Americans could only converse in one language. A random sample of 130 Americans was randomly selected. What is the probability that 100 or fewer of these Americans could only converse in one language?

0.8432

Dover Motors is a car dealership that sells new and used cars. Suppose they sold 140 used cars during the most recent quarter. The average selling price was $10,325 with a standard deviation of $2,880. A random sample of 60 used cars from this population was selected. What is the probability that the sample mean exceeds $10,000?

0.8754

YouTube would like to test the hypothesis that the average length of an online video watched by a user is more than 8 minutes. A random sample of 37 people watched online videos that averaged 8.7 minutes in length. It is believed that the population standard deviation for the length of online videos is 2.5 minutes. YouTube would like to set α = 0.02. The critical value for this hypothesis test would be ________.

2.05

Medicare would like to test the hypothesis that the average monthly rate for one-bedroom assisted-living facility is equal to $3,300. A random sample of 12 assisted-living facilities had an average rate of $3,690 per month. The standard deviation for this sample was $530. Medicare would like to set α = 0.05. The critical value for this hypothesis test would be ________.

2.201

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 ________.

2.583

A random sample of 13 hotels in Tallahassee 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 ________.

6.63

A random sample of 30 business students required an average of 103.4 minutes to complete a QMB 3200 exam. Assume that the population standard deviation to complete the exam was 15.7 minutes. The margin of error for a 98% confidence interval around this sample mean is ________.

6.67

Suppose the average math SAT score for students enrolled at FSU is 570.3 with a standard deviation of 58.2. A random sample of 49 students has been selected. The standard error of the mean for this sample is ________.

8.31

The Central Limit Theorem requires

a sample size of at least 30 be used to ensure that the samples means are normally distributed

Proportion data follow the ________ distribution, which can be approximated by the ________ distribution under the following conditions: nπ ≥ 5 and n(1 - π) ≥ 5.

binomial, normal

Medicare would like to test the hypothesis that the average monthly rate for one-bedroom assisted-living facility is equal to $3,300. A random sample of 12 assisted-living facilities had an average rate of $3,690 per month. The standard deviation for this sample was $530. Medicare would like to set α = 0.05. The conclusion for this hypothesis test would be that because the absolute value of the test statistic is

more than the absolute value of the critical value, we can conclude that the average monthly rate for an assisted-living facility is not equal to $3,300.

The Central Limit Theorem (CLT) states that the sample means

of large-sized samples will be normally distributed regardless of the shape of their population distributions.

A ________ sample is a sample in which each member of the population has a known, nonzero, chance of being selected for the sample.

probability

The p-value for a hypothesis test is defined as the probability of observing a ___________________________________________________.

sample mean at least as extreme as the one selected for the hypothesis test, assuming the null hypothesis is true

As the size of the sample increases, the ________________________________.

standard error of the mean becomes smaller

According to the US Treasury, the average COVID-19 stimulus payment per family was $1,974. Assuming that the standard deviation for these payments was $412, the standard error of the mean for a random sample of 80 tax returns is ________.

$46.06

Killearn Estates is a neighborhood in Tallahassee comprised of a total of 185 homes. According to the website Zillow, the average market value of the homes in this neighborhood is $418,300 with a standard deviation of $36,500. What is the standard error for a random sample of 32 homes from this neighborhood?

$5,883.76

Turkey Town Surfing is an online company that sells surfing materials for avid surfers. Suppose their average order size is $218.19 with a standard deviation of $35.44. A random sample of 35 customer orders has been selected. The standard error of the mean for this sample is ________.

$5.99

A random sample of 13 hotels in Orlando 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 ________.

($151.85, $192.35)

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 ________.

($293.30, $317.30)

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

($372.74, $414.26)

A local church has a total population 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. Further, the population standard deviation is $12.30. The 95% confidence interval to estimate the average weekly donation is ________. Hint: don't forget the finite population correction factor.

($47.62, $53.18)

A random sample of 150 mortgages in the state of Florida 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 ________.

(0.053, 0.174)

Dr. Jordan operates a dental practice with a total population of 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 ________. Hint: don't forget the finite population correction factor.

(0.291, 0.436)

"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 95% confidence interval for the proportion based on this sample is ________.

(0.519, 0.731)

The Department of Transportation would like to test the hypothesis that the average age of cars on the road is less than 12 years. A random sample of 45 cars had an average age of 10.6 years. It is believed that the population standard deviation for the age of cars is 4.1 years. The Department of Transportation would like to set α = 0.05. The p-value for this hypothesis test would be ________.

0.0110

Many franchisers favor owners who operate multiple stores by providing them with preferential treatment. Suppose the Small Business Administration would like to perform a hypothesis test to investigate if 80% of franchisees own only one location using α= 0.05. A random sample of 120 franchisees found that 85 owned only one store. The p-value for this hypothesis test would be ________.

0.0121

A Florida neighborhood is comprised of a total of 250 houses of which 12% are in foreclosure. A random sample of 91 homes from this neighborhood was selected. The standard error of the proportion is ________.

0.0272

The Fortune 500 is comprised of Fortune magazine's annual list of the finite population of the top 500 companies in the U.S. ranked by revenues. According to Catalyst, 16% of positions on corporate boards at Fortune 500 companies were held by women in 2018. A random sample of 100 Fortune 500 companies was selected. The standard error of the proportion is ________.

0.0328

YouTube would like to test the hypothesis that the average length of an online video watched by a user is more than 8 minutes. A random sample of 37 people watched online videos that averaged 8.7 minutes in length. It is believed that the population standard deviation for the length of online videos is 2.5 minutes. YouTube would like to set α = 0.02. The p-value for this hypothesis test would be ________.

0.0443

"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 ________.

0.0541

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 ________.

0.0627

The Department of Education would like to test the hypothesis that the average debt load of graduating students with a Bachelor's degree is equal to $17,000. A random sample of 34 students had an average debt load of $18,200. It is believed that the population standard deviation for student debt load is $4,200. The Department of Education would like to set α = 0.05. The p-value for this hypothesis test would be ________.

0.0957

Breyers is a major producer of ice cream and would like to test the hypothesis that the average American consumes more than 17 ounces if ice cream per month. A random sample of 15 Americans was found to consume an average of 18.2 ounces of ice cream last month. The standard deviation for this sample was 3.9 ounces. Breyers would like to set α = 0.10. The p-value for this hypothesis test would be between ________.

0.10 and 0.20

"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 ________.

0.1061

Many hotel chains that offer free Wi-Fi service to their customers have experienced increasing demand for Internet bandwidth and increasing costs. Marriott International would like to test the hypothesis that the proportion of customers that are carrying two Wi-Fi devices exceeds 0.60. A random sample of 120 Marriott customers found that 78 have two Wi-Fi devices. Marriott International would like to set α = 0.01. The p-value for this hypothesis test would be ________.

0.1318

Recently, FHA mortgages, which are insured by the federal government, accounted for 28% of all home-purchase mortgages that were approved. A random sample of 150 mortgage applications was selected. What is the probability that 48 or more from this sample were insured by the FHA?

0.1376

A statistics class has a population of 140 students of which 55% are female. A random sample of 40 students was selected. What is the probability that 24 or more from this sample will be female?

0.2268

According to R.L. Polk & Co., the average age of cars and light trucks in the U.S. is 10.8 years. Assume that the standard deviation for this population is 3.7 years. A sample of 35 randomly selected vehicles was selected. What is the probability that the sample mean will be greater than 10 years?

0.8996

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

1.318

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

1.41

A random sample of 17 hotels in Orlando had an average nightly room rate of $165.40 with a sample standard deviation of $21.70. The margin of error for a 95% confidence interval around this sample mean is ________.

11.16

Many hotel chains that offer free Wi-Fi service to their customers have experienced increasing demand for Internet bandwidth and increasing costs. Marriott International would like to test the hypothesis that the proportion of customers that are carrying two Wi-Fi devices exceeds 0.60. A random sample of 120 Marriott customers found that 78 have two Wi-Fi devices. Marriott International would like to set α = 0.01. The correct hypothesis statement for this hypothesis test would be ___________________________.

H0: p ≤ 0.60; H1: p > 0.60

YouTube would like to test the hypothesis that the average length of an online video watched by a user is more than 8 minutes. A random sample of 37 people watched online videos that averaged 8.7 minutes in length. It is believed that the population standard deviation for the length of online videos is 2.5 minutes. YouTube would like to set α = 0.02. The correct hypothesis statement for this hypothesis test would be _________________________.

H0: μ ≤ 8.0; H1: μ > 8.0

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

The shape of the Student's t-distribution is narrower than the shape of the normal distribution.

Sampling error is the difference between a sample statistic and a population parameter.

True

The definition of a 90% confidence interval is that we expect that close to 90% of a large number of sample means drawn from a population will produce confidence intervals that include that population's mean.

True

The critical value for a hypothesis test _______________________________.

is based on the significance level and determines the boundary for the rejection region

The National Center for Education Statistics would like to test the hypothesis that the proportion of Bachelor's degrees that were earned by women equals 0.60. A random sample of 140 college graduates with Bachelor degrees found that 75 were women. The National Center for Education Statistics would like to set α = 0.10. The conclusion for this hypothesis test would be that because the absolute value of the test statistic is __________________________________.

less than the absolute value of the critical value, we cannot conclude that the proportion of Bachelor's degrees that were earned by women does not equal 0.60.

The Department of Transportation would like to test the hypothesis that the average age of cars on the road is less than 12 years. A random sample of 45 cars had an average age of 10.6 years. It is believed that the population standard deviation for the age of cars is 4.1 years. The Department of Transportation would like to set α = 0.05. The conclusion for this hypothesis test would be that because the test statistic is ______________________________________.

less than the critical value, we can conclude that the average age of cars on the road is less than 12 years

YouTube would like to test the hypothesis that the average length of an online video watched by a user is more than 8 minutes. A random sample of 37 people watched online videos that averaged 8.7 minutes in length. It is believed that the population standard deviation for the length of online videos is 2.5 minutes. YouTube would like to set α = 0.02. The conclusion for this hypothesis test would be that because the test statistic is _____________________.

less than the critical value, we can conclude that the average length of an online video is not more than 8 minutes

Breyers is a major producer of ice cream and would like to test the hypothesis that the average American consumes more than 17 ounces if ice cream per month. A random sample of 15 Americans was found to consume an average of 18.2 ounces of ice cream last month. The standard deviation for this sample was 3.9 ounces. Breyers would like to set α = 0.10. The conclusion for this hypothesis test would be that because the test statistic is ________________________________.

less than the critical value, we cannot conclude that the average amount of ice cream consumed per month is greater than 17 ounces

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

reduce the margin of error resulting in a narrower (more precise) confidence interval.

The test statistic for a hypothesis test _______________________________.

represents the number of standard deviations between the sample mean and the population mean according to the null hypothesis

Breyers is a major producer of ice cream and would like to test the hypothesis that the average American consumes more than 17 ounces if ice cream per month. A random sample of 15 Americans was found to consume an average of 18.2 ounces of ice cream last month. The standard deviation for this sample was 3.9 ounces. Breyers would like to set α = 0.10. The test statistic for this hypothesis test would be ________.

tx = 1.19

Medicare would like to test the hypothesis that the average monthly rate for one-bedroom assisted-living facility is equal to $3,300. A random sample of 12 assisted-living facilities had an average rate of $3,690 per month. The standard deviation for this sample was $530. Medicare would like to set α = 0.05. The test statistic for this hypothesis test would be ________.

tx = 2.55

The National Center for Education Statistics would like to test the hypothesis that the proportion of Bachelor's degrees that were earned by women equals 0.60. A random sample of 140 college graduates with Bachelor degrees found that 75 were women. The National Center for Education Statistics would like to set α = 0.10. The test statistic for this hypothesis test would be ________.

zp = -1.55

Many hotel chains that offer free Wi-Fi service to their customers have experienced increasing demand for Internet bandwidth and increasing costs. Marriott International would like to test the hypothesis that the proportion of customers that are carrying two Wi-Fi devices exceeds 0.60. A random sample of 120 Marriott customers found that 78 have two Wi-Fi devices. Marriott International would like to set α = 0.01. The test statistic for this hypothesis test would be _______.

zp = 1.12

The Department of Transportation would like to test the hypothesis that the average age of cars on the road is less than 12 years. A random sample of 45 cars had an average age of 10.6 years. It is believed that the population standard deviation for the age of cars is 4.1 years. The Department of Transportation would like to set α = 0.05. The test statistic for this hypothesis test would be ________.

zx = -2.29

The Department of Education would like to test the hypothesis that the average debt load of graduating students with a Bachelor's degree is equal to $17,000. A random sample of 34 students had an average debt load of $18,200. It is believed that the population standard deviation for student debt load is $4,200. The Department of Education would like to set α = 0.05. The test statistic for this hypothesis test would be ________.

zx = 1.67

YouTube would like to test the hypothesis that the average length of an online video watched by a user is more than 8 minutes. A random sample of 37 people watched online videos that averaged 8.7 minutes in length. It is believed that the population standard deviation for the length of online videos is 2.5 minutes. YouTube would like to set α = 0.02. The test statistic for this hypothesis test would be ________.

zx = 1.70

The critical value for an 84% confidence interval for the proportion is ________. Hint: this is nothing more than the absolute value of Z-alpha/2.

± 1.41