Exam 9: Hypothesis Tests

A student believes that the average grade on the statistics final examination was 87.A sample of 36 final examinations was taken.The average grade in the sample was 83.96 with a standard deviation of 12. a.State the null and alternative hypotheses. b.Using the critical value approach,test the hypotheses at the 5% level of significance. c.Using the p-value approach,test the hypotheses at the 5% level of significance.

In a two-tailed hypothesis test the test statistic is determined to be Z = -2.5.The p-value for this test is

A two-tailed test is performed at 95% confidence.The p-value is determined to be 0.09.The null hypothesis

Exhibit 9-5 A random sample of 100 people was taken.Eighty-five of the people in the sample favored Candidate A.We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 80%. -Refer to Exhibit 9-5.The p-value is

Exhibit 9-7 A random sample of 16 statistics examinations from a large population was taken.The average score in the sample was 78.6 with a variance of 64.We are interested in determining whether the average grade of the population is significantly more than 75.Assume the distribution of the population of grades is normal. -Refer to Exhibit 9-7.The test statistic is

Confirmed cases of West Nile virus in birds for a sample of six counties in the state of Georgia are shown below. We are interested in testing the following hypotheses regarding these data: H₀: $\mu$ 3 H_a: $\mu$ > 3 a.Compute the mean and the standard deviation of the sample. b.Compute the standard error of the mean. c.Determine the test statistic. d.Determine the p-value and at 95% confidence,test the hypotheses.

The manager of an automobile dealership is considering a new bonus plan in order to increase sales.Currently,the mean sales rate per salesperson is five automobiles per month.The correct set of hypotheses for testing the effect of the bonus plan is

Ahmadi,Inc.has been manufacturing small automobiles that have averaged 50 miles per gallon of gasoline in highway driving.The company has developed a more efficient engine for its small cars and now advertises that its new small cars average more than 50 miles per gallon in highway driving.An independent testing service road-tested 64 of the automobiles.The sample showed an average of 51.5 miles per gallon with a standard deviation of 4 miles per gallon. a.Formulate the hypotheses to determine whether or not the manufacturer's advertising campaign is legitimate. b.Compute the test statistic. c.What is the p-value associated with the sample results and what is your conclusion? Let $\alpha$ = .05.

If the probability of a Type I error ( $\alpha$ )is 0.05,then the probability of a Type II error ( $\beta$ )must be

In the last presidential election,a national survey company claimed that no more than 50% (i.e. ,< 50%)of all registered voters voted for the Republican candidate.In a random sample of 400 registered voters,208 voted for the Republican candidate. a.State the null and the alternative hypotheses. b.Compute the test statistic. c.At 95% confidence,compute the p-value and test the hypotheses.

The school's newspaper reported that the proportion of students majoring in business is at least 30%.You plan on taking a sample to test the newspaper's claim.The correct set of hypotheses is

For a one-tailed test (lower tail)at 93.7% confidence,Z =

In the past,the average age of employees of a large corporation has been 40 years.Recently,the company has been hiring older individuals.In order to determine whether there has been an increase in the average age of all the employees,a sample of 64 employees was selected.The average age in the sample was 45 years with a standard deviation of 16 years.Let $\alpha$ = .05. a.State the null and the alternative hypotheses. b.Compute the test statistic. c.Using the p-value approach,test to determine whether or not the mean age of all employees is significantly more than 40 years.

Exhibit 9-3 -Refer to Exhibit 9-3.If the test is done at the 5% level of significance,the null hypothesis should

Exhibit 9-8 The average gasoline price of one of the major oil companies in Europe has been $1.25 per liter.Recently,the company has undertaken several efficiency measures in order to reduce prices.Management is interested in determining whether their efficiency measures have actually reduced prices.A random sample of 49 of their gas stations is selected and the average price is determined to be $1.20 per liter.Furthermore,assume that the standard deviation of the population ( )is $0.14. -Refer to Exhibit 9-8.The standard error has a value of

For a two-tail test,the p-value is the probability of obtaining a value for the test statistic as

The probability of making a Type I error is denoted by

Your investment executive claims that the average yearly rate of return on the stocks she recommends is at least 10.0%.You plan on taking a sample to test her claim.The correct set of hypotheses is

In the hypothesis testing procedure, $\alpha$ is

For a lower tail test,the p-value is the probability of obtaining a value for the test statistic