Exam 9: Hypothesis Tests

You are given the following information obtained from a random sample of 5 observations. Assume the population has a normal distribution. 20 18 17 22 18 You want to determine whether or not the mean of the population from which this sample was taken is significantly less than 21. a. State the null and the alternative hypotheses. b. Compute the standard error of the mean. c. Determine the test statistic. d. Determine the p-value and at 90% confidence, test whether or not the mean of the population is significantly less than 21.

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

Automobiles manufactured by the Efficiency Company have been averaging 42 miles per gallon of gasoline in highway driving. It is believed that its new automobiles average more than 42 miles per gallon. An independent testing service road-tested 36 of the automobiles. The sample showed an average of 42.8 miles per gallon with a standard deviation of 1.2 miles per gallon. a. With a 0.05 level of significance using the critical value approach, test to determine whether or not the new automobiles actually do average more than 42 miles per gallon. b. What is the p-value associated with the sample results? What is your conclusion based on the p-value?

In hypothesis testing,

"D" size batteries produced by MNM Corporation have had a life expectancy of 87 hours. Because of an improved production process, it is believed that there has been an increase in the life expectancy of its "D" size batteries. A sample of 36 batteries showed an average life of 88.5 hours. Assume from past information that it is known that the standard deviation of the population is 9 hours. a. Formulate the hypotheses for this problem. b. Compute the test statistic. c. What is the p-value associated with the sample results? What is your conclusion based on the p-value? Let α = .05.

A student believes that no more than 20% i.e., ≤ 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.

It is said that more males register to vote in a national election than females. A research organization selected a random sample of 300 registered voters and reported that 165 of the registered voters were male. a. Formulate the hypotheses for this problem. b. Compute the standard error of . c. Compute the test statistic. d. Using the p-value approach, can you conclude that more males registered to vote than females? Let α = .05.

A student believes that the average grade on the final examination in statistics is at least 85. She plans on taking a sample to test her belief. The correct set of hypotheses is

The academic planner of a university thinks that at least 35% of the entire student body attends summer school. The correct set of hypotheses to test his belief is

Exhibit 9-3 n = 49 = 54.8 s = 28 H0: μ ≤ 50 Ha: μ > 50 -Refer to Exhibit 9-3. The p-value is between

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 σ) 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.

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 α = .05.

Exhibit 9-3 n = 49 = 54.8 s = 28 H0: μ ≤ 50 Ha: μ > 50 -Refer to Exhibit 9-3. If the test is done at the 5% level of significance, the null hypothesis should

A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink. Any over filling or under filling results in the shutdown and readjustment of the machine. To determine whether or not the machine is properly adjusted, the correct set of hypotheses is

A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink. A random sample of 49 bottles is selected, and the contents are measured. The sample yielded a mean content of 11.88 ounces with a standard deviation of 0.35 ounces. a. Formulate the hypotheses to test to determine if the machine is in perfect adjustment. b. Compute the value of the test statistic. c. Compute the p-value and give your conclusion regarding the adjustment of the machine. Let α = .05.

A producer of various kinds of batteries has been producing "D" size batteries with a life expectancy of 87 hours. Due to an improved production process, management believes that there has been an increase in the life expectancy of their "D" size batteries. A sample of 36 batteries showed an average life of 88.5 hours. Assume from past information that it is known that the standard deviation of the population is 9 hours. a. Give the null and the alternative hypotheses. b. Compute the test statistic. c. At 99% confidence using the critical value approach, test management's belief. d. What is the p-value associated with the sample results? What is your conclusion based on the p-value?

An official of a large national union claims that the fraction of women in the union is not significantly different from one-half. Using the critical value approach and the sample information reported below, carry out a test of this statement. Let α = 0.05. sample size 400 women 168 men 232

The p-value

The level of significance is the

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 σ) is $0.14. -Refer to Exhibit 9-8. The standard error has a value of