CHP 9 QUIZ STA 2023 McGraw Hill

On the basis of sample information, we either "accept the null hypothesis" or "reject the null hypothesis." True

False On the basis of sample information, we either "reject the null hypothesis" or "do not reject the null hypothesis." Only one of two hypotheses is true and the hypotheses cover all possible values of the population parameter.

A university interested in tracking its honors program believes that the proportion of graduates with a GPA of 3.00 or below is less than 0.20. In a sample of 200 graduates, 30 students have a GPA of 3.00 or below. In testing the university's belief, how does one define the population parameter of interest?

It's the proportion of honors graduates with a GPA of 3.00 or below. The parameter to be tested is the population proportion of honors graduates.

What is the decision rule when using the p-value approach to hypothesis testing?

Reject Ho if the p-value < α.

The national average for an eighth-grade reading comprehension test is 73. A school district claims that its eighth-graders outperform the national average. In testing the school district's claim, how does one define the population parameter of interest?

The mean score on the eighth-grade reading comprehension test Hypothesis testing is used to resolve conflicts between two competing hypotheses on a particular population parameter of interest.

When we reject the null hypothesis when it is actually false, we have committed _________.

no error

A local courier service advertises that its average delivery time is less than 6 hours for local deliveries. When testing the two hypotheses, Ho:μ ≥ 6 and HA:μ < 6, μ stand for _____________.

the mean delivery time Hypothesis testing is used to resolve conflicts between two competing hypotheses on a particular population parameter of interest.

If the chosen significance level is α = 0.05, then ____________________________________________.

there is a 5% probability of rejecting a true null hypothesis The significance level is the probability of committing a Type I error, which is the probability of rejecting the null hypothesis when the null hypothesis is true.

The null hypothesis typically corresponds to a presumed default state of nature.

True

On the basis of sample information, we either "accept the null hypothesis" or "reject the null hypothesis."

False On the basis of sample information, we either "reject the null hypothesis" or "do not reject the null hypothesis." Only one of two hypotheses is true and the hypotheses cover all possible values of the population parameter.

A newly hired basketball coach promised a high-paced attack that will put more points on the board than the team's previously tepid offense historically managed. After a few months, the team owner looks at the data to test the coach's claim. He takes a sample of 36 of the team's games under the new coach and finds that they scored an average of 101 points with a standard deviation of 6 points. Over the past 10 years, the team had averaged 99 points. What is(are) the appropriate critical value(s) to test the new coach's claim at the 1% significance level?

2.438 For a right-tailed test with α = 0.05 and df = n - 1, the critical value is tα,df and is defined using t table.

Which of the following are one-tailed tests?

Both Ho:μ ≤ 10, HA:μ > 10 and Ho:μ ≥ 400, HA:μ < 400 A two-tailed test is defined when the alternative hypothesis includes the sign "≠". A one-tailed test involves a null hypothesis that can be rejected only on one side of hypothesized value.

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. In 2009, 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. When testing whether the dropout rate has decreased, the appropriate hypotheses are _____________

Ho: p greater than or equal to 0.081, Ha: p <0.081 The competing hypotheses are Ho: p ≥ po,HA: < po. It is referred to as a left-tailed test of the population proportion.

Which of the following represents an appropriate set of hypotheses?

Ho:u=0 , Ha cannot equal 0 A parameter is always tested, the null and alternative hypotheses must be mutually exclusive and collectively exhaustive, and the equal sign must appear in the null hypothesis.

What type of data would necessitate using a hypothesis test of the population proportion rather than a test of the population mean?

Qualitative The population proportion p is the essential descriptive measure when the data type is qualitative.

What is the decision rule when using the p-value approach to hypothesis testing?

Reject Ho if the p-value < α. The decision rule is to reject the null hypothesis if the p-value < α and not reject the null hypothesis if the p-value ≥ α.

Which of the following answers represents the objective of a hypothesis test?

Rejecting the null hypothesis when it is false and not rejecting the null hypothesis when it is true. Two correct decisions are possible: not rejecting the null hypothesis when the null hypothesis is true and rejecting the null hypothesis when the null hypothesis is false. Rejecting the null hypothesis when it is false and not rejecting the null hypothesis when it is true includes both types of correct decisions.

When conducting a hypothesis test, which of the following decisions represents an error?

Rejecting the null hypothesis when it is true. A Type I error is committed when we reject the null hypothesis when the null hypothesis is actually true. A Type II error is made when we do not reject the null hypothesis and the null hypothesis and the null hypothesis is actually false.

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, 2011). But Keurig's patent on K-cups, the plastic pods used to brew the coffee, is expected to expire in 2012, 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. Which of the following should be used to develop the null and alternative hypotheses to test this claim?

p is less than or equal to 0.47, Ha: p>0.47 The competing hypotheses are Ho: p ≥ po,HA: < po. It is referred to as a left-tailed test of the population proportion.

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: Ho: μ ≤ 300. HA: μ > 300. The consequences of committing a Type I error would be that____________________________.

the franchiser builds on an unacceptable site A Type I error is committed when we reject the null hypothesis when the null hypothesis is actually true.

The owner of a large car dealership believes that the financial crisis decreased the number of customers visiting her dealership. The dealership has historically had 800 customers per day. The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 750. Assume that the population standard deviation is 350. The population parameter to be tested is ___________.

the mean number of customers visiting the dealership per day The parameter to be tested is the mean number of customers visiting the dealership per day.

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, 2011). But Keurig's patent on K-cups, the plastic pods used to brew the coffee, is expected to expire in 2012, 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?

z = 0.721 When testing the population proportion, the value of the test statistic is computed as formula54.mml

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. In 2009, 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. The value of the test statistic is ____________.

z=-1.854 When testing the population proportion, the value of the test statistic is computed as formula54.mml