Exam 9: Hypothesis Tests

The average gasoline price of one of the major oil companies has been $2.20 per gallon.Because of cost reduction measures,it is believed that there has been a significant reduction in the average price.In order to test this belief,we randomly selected a sample of 36 of the company's gas stations and determined that the average price for the stations in the sample was $2.14.Assume that the standard deviation of the population (H₀)is $0.12. a.State the null and the alternative hypotheses. b.Compute the test statistic. c.What is the p-value associated with the above sample results? d.At 95% confidence,test the company's claim.

For a two-tailed test at 86.12% confidence,Z =

Exhibit 9-1 -Refer to Exhibit 9-1.The p-value is between

In the past,75% of the tourists who visited Chattanooga went to see Rock City.The management of Rock City recently undertook an extensive promotional campaign.They are interested in determining whether the promotional campaign actually increased the proportion of tourists visiting Rock City.The correct set of hypotheses is

The probability of committing a Type I error when the null hypothesis is true is

Exhibit 9-1 -Refer to Exhibit 9-1.If the test is done at 95% confidence,the null hypothesis should

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

Consider the following hypothesis test: H_o: $\mu$ = 10 H_a: $\mu$ $\neq$ 10 A sample of 81 provides a sample mean of 9.5 and a sample standard deviation of 1.8. a.Determine the standard error of the mean. b.Compute the value of the test statistic. c.Determine the p-value;and at 95% confidence,test the above hypotheses.

At a local university,a sample of 49 evening students was selected in order to determine whether the average age of the evening students is significantly different from 21.The average age of the students in the sample was 23 with a standard deviation of 3.5. a.Formulate the hypotheses for this problem. b.Compute the test statistic. c.Determine the p-value and test these hypotheses.Let $\alpha$ = .05.

The error of rejecting a true null hypothesis is

If the level of significance of a hypothesis test is raised from .01 to .05,the probability of a Type II error

Read the Z statistic from the normal distribution table and circle the correct answer.A one-tailed test (upper tail)at 87.7% confidence;Z =

Exhibit 9-9 The sales of a grocery store had an average of $8,000 per day.The store introduced several advertising campaigns in order to increase sales.To determine whether or not the advertising campaigns have been effective in increasing sales,a sample of 64 days of sales was selected.It was found that the average was $8,300 per day.From past information,it is known that the standard deviation of the population is $1,200. -Refer to Exhibit 9-9.The p-value is

Consider the following hypothesis test: H_o: p = 0.5 H_a: p $\neq$ 0.5 A sample of 800 provided a sample proportion of 0.58. a.Determine the standard error of the proportion. b.Compute the value of the test statistic. c.Determine the p-value,and at 95% confidence,test the hypotheses.

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.At 95% confidence,it can be concluded that the average grade of the population

For a lower bounds one-tailed test,the test statistic z is determined to be zero.The p-value for this test is

In a one-tailed hypothesis test (lower tail)the test statistic is determined to be -2.The p-value for this test is

Last year,a soft drink manufacturer had 21% of the market.In order to increase their portion of the market,the manufacturer has introduced a new flavor in their soft drinks.A sample of 400 individuals participated in the taste test and 100 indicated that they like the taste.We are interested in determining if more than 21% of the population will like the new soft drink. a.Set up the null and the alternative hypotheses. b.Determine the test statistic. c.Determine the p-value. d.At 95% confidence,test to determine if more than 21% of the population will like the new soft drink.

A student believes that no more than 20% (i.e. , $\le$ 20%)of the students who finish a statistics course get an A.A random sample of 100 students was taken.Twenty-four percent of the students in the sample received A's. a.State the null and alternative hypotheses. b.Using the critical value approach,test the hypotheses at the 1% level of significance. c.Using the p-value approach,test the hypotheses at the 1% level of significance.

Identify the null and alternative hypotheses for the following problems. a.The manager of a restaurant believes that it takes a customer less than or equal to 25 minutes to eat lunch. b.Economists have stated that the marginal propensity to consume is at least 90¢ out of every dollar. c.It has been stated that 75 out of every 100 people who go to the movies on Saturday night buy popcorn.