Exam 9: Hypothesis Tests

Consider the following hypothesis test: H_o: $\mu$ 40 H_a: $\mu$ < 40 A sample of 49 provides a sample mean of 38 and a sample standard deviation of 7. 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.

Two thousand numbers are selected randomly; 960 were even numbers. a.State the hypotheses to determine whether the proportion of odd numbers is significantly different from 50%. b.Compute the test statistic. c.At 90% confidence using the p-value approach, test the hypotheses.

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

Exhibit 9-1 n = 36 = 24.6 S = 12 H₀: $\mu$ 20 H_a: $\mu$ > 20 -Refer to Exhibit 9-1. The p-value is between

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 value of the test statistic for this hypothesis test is

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

The level of significance in hypothesis testing is the probability of

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

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

A group of young businesswomen wish to open a high fashion boutique in a vacant store but only if the average income of households in the area is at least $25,000. A random sample of 9 households showed the following results. $28,000 $24,000 $26,000 $25,000 $23,000 $27,000 $26,000 $22,000 $24,000 Assume the population of incomes is normally distributed. a.Compute the sample mean and the standard deviation. b.State the hypotheses for this problem. c.Compute the test statistic. d.At 95% confidence using the p-value approach, what is your conclusion?

Nancy believes that the average running time of movies is equal to 140 minutes. A sample of 4 movies was taken and the following running times were obtained. Assume the population of the running times is normally distributed.150 150 180 170 a.Compute the sample mean and the standard deviation. b.State the null and alternative hypotheses. c.Using the critical value approach, test the hypotheses at the 10% level of significance. d.Using the p-value approach, test the hypotheses at the 10% level of significance.

UHON Research Group has tested the hypotheses regarding the IQ of university honor students. They provided the following information. H_o: µ_o = 144 H_a: µ_o > 144 (Genius) P-Value = 0.0054 Sample Mean = 145 Sample size n = 121 a.At 98.5% confidence, would you reject or not reject the null hypothesis? Explain how you arrived at your answer and what you can conclude about the IQ scores of UHON students? b.The researchers failed to report the standard deviation. Determine the standard deviation. Use the normal distribution tables to answer this question and show your complete work.

A sample of 1400 items had 280 defective items. For the following hypothesis test, H_o: P = 0.20 H_a: P > 0.20 The test statistic 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

You are given the following information obtained from a random sample of 4 observations. 25 47 32 56 You want to determine whether or not the mean of the population from which this sample was taken is significantly different from 48. (Assume the population is normally distributed.) a.State the null and the alternative hypotheses. b.Determine the test statistic. c.Determine the p-value; and at 95% confidence test to determine whether or not the mean of the population is significantly different from 48.

What type of error occurs if you fail to reject H₀ when, in fact, it is not true?

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.

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

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

For a one-tailed test (upper tail), a sample size of 26 at 90% confidence, t =