QUIZ 3 Sampling and Hypothesis Testing

a true null hypothesis is rejected

A Type I error is committed when _____

the franchiser builds on an unacceptable site

A fast-food franchise is considering building a restaurant at a busy intersection. A financial advisor determines that the site is acceptable only if, on average, more than 300 automobiles pass the location per hour. The advisor tests the following hypotheses: H0: μ ≤ 300. HA: μ > 300. The consequences of committing a Type I error would be that __________.

both the underlying population is normal and the sample size n ≥ 30 are correct

According to the central limit theorem, the distribution of the sample means is normal if ________.

is closer to a normal distribution

The central limit theorem states that, for any distribution, as n gets larger, the sampling distribution of the sample mean ______.

the franchiser does not build on an acceptable site

A fast-food franchise is considering building a restaurant at a busy intersection. A financial advisor determines that the site is acceptable only if, on average, more than 300 automobiles pass the location per hour. The advisor tests the following hypotheses: H0: μ ≤ 300. HA: μ > 300. The consequences of committing a Type II error would be that

1.85

A nursery sells trees of different types and heights. These trees average 60 inches in height with a standard deviation of 16 inches. Suppose that 75 pine trees are sold for planting at City Hall. What is the standard deviation for the sample mean?

2.15

A nursery sells trees of different types and heights. These trees average 90 inches in height with a standard deviation of 18 inches. Suppose that 70 pine trees are sold for planting at City Hall. What is the standard deviation for the sample mean?

Type I: 4%, Type II: 6%

A professional sports organization is going to implement a test for steroids. The test gives a positive reaction in 94% of the people who have taken the steroid. However, it erroneously gives a positive reaction in 4% of the people who have not taken the steroid. What is the probability of Type I and Type II errors giving the null hypothesis "the individual has not taken steroids."

rejects the null hypothesis and concludes that the mean retirement age has increased

A recent report claimed that Americans are retiring later in life (U.S. News & World Report, August 17). An economist wishes to determine if the mean retirement age has increased from 62. To conduct the relevant test, she takes a random sample of 38 Americans who have recently retired and computes the value of the test statistic as t37 = 1.92. With α = 0.05, she __________.

1%

A statistics professor works tirelessly to catch students cheating on his exams. He has particular routes for his teaching assistants to patrol, an elevated chair to ensure an unobstructed view of all students, and even a video recording of the exam in case additional evidence needs to be collected. He estimates that he catches 95% of students who cheat in his class, but 1% of the time that he accuses a student of cheating he is actually incorrect. Consider the null hypothesis, "the student is not cheating." What is the probability of a Type I error?

0.77.

A television network is deciding whether or not to give its newest television show a spot during prime viewing time at night. If this is to happen, it will have to move one of its most viewed shows to another slot. The network conducts a survey asking its viewers which show they would rather watch. The network receives 812 responses, of which 417 indicate that they would like to see the new show in the lineup. The test statistic for this hypothesis would be __________.

1.01

A television network is deciding whether or not to give its newest television show a spot during prime viewing time at night. If this is to happen, it will have to move one of its most viewed shows to another slot. The network conducts a survey asking its viewers which show they would rather watch. The network receives 827 responses, of which 428 indicate that they would like to see the new show in the lineup. The test statistic for this hypothesis would be __________.

H0: p ≤ 0.50, HA: p > 0.50

A television network is deciding whether or not to give its newest television show a spot during prime viewing time at night. If this is to happen, it will have to move one of its most viewed shows to another slot. The network conducts a survey asking its viewers which show they would rather watch. The network receives 827 responses, of which 428 indicate they would like to see the new show in the lineup. Which of the following is an appropriate hypotheses to test if the television network should give its newest show a spot during prime time at night?

the mean GPA of the university honors students

A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. The population standard deviation is assumed to equal 0.40. The parameter to be tested is __________.

the mean GPA of the university honors students

A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 4.70. A sample of 41 honors students is taken and is found to have a mean GPA equal to 4.80. The population standard deviation is assumed to equal 0.40. The parameter to be tested is __________.

1.4142

An advertisement for a popular weight-loss clinic suggests that participants in its new diet program lose, on average, more than 10 pounds. A consumer activist decides to test the authenticity of the claim. She follows the progress of 18 women who recently joined the weight-reduction program. She calculates the mean weight loss of these participants as 10.8 pounds with a standard deviation of 2.4 pounds. The test statistic for this hypothesis would be __________.

H0:µ ≤ µ0 , HA:µ > µ0

An advertisement for a popular weight-loss clinic suggests that participants in its new diet program lose, on average, more than 10 pounds. A consumer activist decides to test the authenticity of the claim. She follows the progress of 18 women who recently joined the weight-reduction program. She calculates the mean weight loss of these participants as 10.8 pounds with a standard deviation of 2.4 pounds. Which of the following are appropriate hypotheses to test the advertisement's claim?

1.1780

An advertisement for a popular weight-loss clinic suggests that participants in its new diet program lose, on average, more than 12 pounds. A consumer activist decides to test the authenticity of the claim. She follows the progress of 17 women who recently joined the weight-reduction program. She calculates the mean weight loss of these participants as 12.8 pounds with a standard deviation of 2.8 pounds. The test statistic for this hypothesis would be __________.

alternative hypothesis

As a general guideline, the research hypothesis should be stated as the _____

It is smaller and therefore suggests that averages have less variation than individual observations.

How does the variance of the sample mean compare to the variance of the population?

For any sample size n, the sampling distribution of the sample mean is normally distributed.

If a population is known to be normally distributed, what can be said of the sampling distribution of the sample mean drawn from this population?

mutually exclusive

In general, the null and alternative hypotheses are __________.

smaller p-values

More evidence against H0 is indicated by _____.

0.8860

Over the entire six years that students attend an Ohio elementary school, they are absent, on average, 28 days due to influenza. Assume that the standard deviation over this time period is σ = 9 days. Upon graduation from elementary school, a random sample of 36 students is taken and asked how many days of school they missed due to influenza. The probability that the sample mean is between 25 and 30 school days is _______.

0.9088

Over the entire six years that students attend an Ohio elementary school, they are absent, on average, 28 days due to influenza. Assume that the standard deviation over this time period is σ = 9 days. Upon graduation from elementary school, a random sample of 36 students is taken and asked how many days of school they missed due to influenza. The probability that the sample mean is less than 30 school days is ______.

28

Over the entire six years that students attend an Ohio elementary school, they are absent, on average, 28 days due to influenza. Assume that the standard deviation over this time period is σ = 9 days. Upon graduation from elementary school, a random sample of 36 students is taken and asked how many days of school they missed due to influenza. What is the expected value for the sampling distribution of the average number of school days missed due to influenza?

1.50

Over the entire six years that students attend an Ohio elementary school, they are absent, on average, 28 days due to influenza. Assume that the standard deviation over this time period is σ = 9 days. Upon graduation from elementary school, a random sample of 36 students is taken and asked how many days of school they missed due to influenza. What is the standard deviation for the sampling distribution of the average number of school days missed due to influenza?

Cannot be determined.

Professor Elderman has given the same multiple-choice final exam in his Principles of Microeconomics class for many years. After examining his records from the past 10 years, he finds that the scores have a mean of 76 and a standard deviation of 12. What is the probability that a class of 15 students will have a class average greater than 70 on Professor Elderman's final exam?

0.9975

Professor Elderman has given the same multiple-choice final exam in his Principles of Microeconomics class for many years. After examining his records from the past 10 years, he finds that the scores have a mean of 89 and a standard deviation of 19.What is the probability that a class of 36 students will have an average greater than 80 on Professor Elderman's final exam?

estimate

Statistics are used to estimate population parameters, particularly when it is impossible or too expensive to poll an entire population. A particular value of a statistic is referred to as a(n) ______.

0.5889

Suppose that, on average, electricians earn approximately µ = $54,000 per year in the United States. Assume that the distribution for electricians' yearly earnings is normally distributed and that the standard deviation is σ = $12,000 dollars. What is the probability that the average salary of four randomly selected electricians is more than $50,000 but less than $60,000?

0.1587

Suppose that, on average, electricians earn approximately µ = $54,000 per year in the United States. Assume that the distribution for electricians' yearly earnings is normally distributed and that the standard deviation is σ = $12,000. What is the probability that the average salary of four randomly selected electricians exceeds $60,000?

0.2525

Suppose that, on average, electricians earn approximately µ = $54,000 per year in the United States. Assume that the distribution for electricians' yearly earnings is normally distributed and that the standard deviation is σ = $12,000. What is the probability that the average salary of four randomly selected electricians is less than $50,000?

6,000

Suppose that, on average, electricians earn approximately µ = $54,000 per year in the United States. Assume that the distribution for electricians' yearly earnings is normally distributed and that the standard deviation is σ = $12,000.Given a sample of four electricians, what is the standard deviation for the sampling distribution of the sample mean?

2,540

Suppose that, on average, electricians earn approximately µ = $54,900 per year in the United States. Assume that the distribution for electricians' yearly earnings is normally distributed and that the standard deviation is σ = $12,700.Given a sample of twenty-five electricians, what is the standard deviation for the sampling distribution of the sample mean?

0.2559

Susan has been on a bowling team for 10 years. After examining all of her scores over that period of time, she finds that they follow a normal distribution. Her average score is 228, with a standard deviation of 17.What is the probability that in a one-game playoff, her score is more than 232?

0.4244

Susan has been on a bowling team for 14 years. After examining all of her scores over that period of time, she finds that they follow a normal distribution. Her average score is 225, with a standard deviation of 13. What is the probability that in a one-game playoff, her score is more than 227?

p-value < 0.05, reject the null hypothesis

The Institute of Education Sciences measures the high school dropout rate as the percentage of 16- through 24-year-olds who are not enrolled in school and have not earned a high school credential. Last year, the high school dropout rate was 8.1%. A polling company recently took a survey of 1,000 people between the ages of 16 and 24 and found that 6.5% of them are high school dropouts. The polling company would like to determine whether the dropout rate has decreased. At a 5% significance level, the decision is to __________.

p-value =0.0318 alpha = 0.05

The Institute of Education Sciences measures the high school dropout rate as the percentage of 16- through 24-year-olds who are not enrolled in school and have not earned a high school credential. Last year, the high school dropout rate was 8.1%. A polling company recently took a survey of 1,000 people between the ages of 16 and 24 and found that 6.5% of them are high school dropouts. The polling company would like to determine whether the dropout rate has decreased. At a 5% significance level, the p-value and α are __________.

z = −1.8545

The Institute of Education Sciences measures the high school dropout rate as the percentage of 16- through 24-year-olds who are not enrolled in school and have not earned a high school credential. Last year, the high school dropout rate was 8.1%. A polling company recently took a survey of 1,000 people between the ages of 16 and 24 and found that 6.5% of them are high school dropouts. The polling company would like to determine whether the dropout rate has decreased. At a 5% significance level, the test statistic is __________.

contests the status quo, for which a corrective action may be required

The alternative hypothesis typically __________.

The p-value = p( ≥ 7.5) = P(Z ≥ 2.434) = 0.0075

The birth weight for babies is normally distributed with a mean of 7.5 lb and a standard deviation of 1.125 lb. Suppose a pediatrician claims that the average birth weight for babies under her care is greater than 7.5 lb. She randomly selects 30 newborns and produces an average birth weight of 8 lb. Which of the following is true if the pediatrician uses a p-value approach to implement a hypothesis test at a 5% significance level to support her claim?

the default state of nature

The null hypothesis in a hypothesis test refers to __________.

p-value and critical value

Two approaches to drawing a conclusion in a hypothesis test are _____.

z = 0.721

Vermont-based Green Mountain Coffee Roasters dominates the market for single-serve coffee in the United States, with its subsidiary Keurig accounting for approximately 70% of sales ("Rivals Try to Loosen Keurig's Grip on Single-Serve Coffee Market," Chicago Tribune, February 26). But Keurig's patent on K-cups, the plastic pods used to brew the coffee, is expected to expire this year, allowing other companies to better compete. Suppose a potential competitor has been conducting blind taste tests on its blend and finds that 47% of consumers strongly prefer its French Roast to that of Green Mountain Coffee Roasters. After tweaking its recipe, the competitor conducts a test with 144 tasters, of which 72 prefer its blend. The competitor claims that its new blend is preferred by more than 47% of consumers to Green Mountain Coffee Roasters' French Roast. What is the value of the appropriate test statistic to test this claim?

less than or equal to the test statistic

When the rejection region is in the lower tail of the sampling distribution, the p-value is the area under the curve _____.

H0: μ < 0

Which of the following hypotheses is not a valid null hypothesis? H0: μ ≤ 0 H0: μ = 0 H0: μ < 0 H0: μ ≥ 0