Ch 9: stats

a true alternative hypothesis is mistakenly rejected

A Type II error is committed when

H0: μ = 5.8 Ha: μ ≠ 5.8

A machine is designed to fill toothpaste tubes with 5.8 ounces of toothpaste. The manufacturer does not want any underfilling or overfilling. The correct hypotheses to be tested are:

H0: μ = 12 Ha: μ ≠ 12

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

H0: μ >= 85 Ha: μ < 85

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

H0: μ >= 80 Ha: μ < 80

A weatherman stated that the average temperature during July in Chattanooga is less than 80 degrees. A sample of 32 Julys is taken. The correct set of hypotheses is

be rejected

Exhibit 9-1 n = 36 = 24.6 S = 12 H0: μ 20 Ha: μ > 20 Refer to Exhibit 9-1. If the test is done at 95% confidence, the null hypothesis should

0.01 to 0.025

Exhibit 9-1 n = 36 = 24.6 S = 12 H0: μ 20 Ha: μ > 20 Refer to Exhibit 9-1. The p-value is between

2.3

Exhibit 9-1 n = 36 = 24.6 S = 12 H0: μ 20 Ha: μ > 20 Refer to Exhibit 9-1. The test statistic is

be rejected

Exhibit 9-2 n = 64 = 50 s = 16 H0: μ 54 Ha: μ < 54 Refer to Exhibit 9-2. If the test is done at 95% confidence, the null hypothesis should

.01 to .025

Exhibit 9-2 n = 64 = 50 s = 16 H0: μ 54 Ha: μ < 54 Refer to Exhibit 9-2. The p-value is between

-2

Exhibit 9-2 n = 64 = 50 s = 16 H0: μ 54 Ha: μ < 54 Refer to Exhibit 9-2. The test statistic equals

significantly greater than 3

Exhibit 9-4 The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes with a standard deviation of 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. Refer to Exhibit 9-4. At 95% confidence, it can be concluded that the mean of the population is

.01 to .025

Exhibit 9-4 The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes with a standard deviation of 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. Refer to Exhibit 9-4. The p-value is between

2.00

Exhibit 9-4 The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes with a standard deviation of 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. Refer to Exhibit 9-4. The test statistic is

is not significantly greater than 80%

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. At 95% confidence, it can be concluded that the proportion of the population in favor of candidate A

0.1056

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

1.25

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 test statistic is

0.0062

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 (s) is $0.14. Refer to Exhibit 9-8. The p-value for this problem is

-2.5

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 (s) is $0.14. Refer to Exhibit 9-8. The value of the test statistic for this hypothesis test is

0.02

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

μ < 8000

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 $8,250 per day. From past information, it is known that the standard deviation of the population is $1,200. Refer to Exhibit 9-9. The correct null hypothesis for this problem is

0.0475

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 $8,250 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

1.67

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 $8,250 per day. From past information, it is known that the standard deviation of the population is $1,200. Refer to Exhibit 9-9. The value of the test statistic is

+0.5

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

at least as small as that provided by the sample

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

-1.27

For a one-tailed test (lower tail) at 89.8% confidence, Z=

unlikely as that provided by the sample

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

2.41

For a two-tailed test at 98.4% confidence, Z=

-0.849

In a one-tailed hypothesis test situation, the p-value is determined to be 0.2. If the sample size for the test is 51, the t statistic has the value of:

the correct decision has been made

In hypothesis testing if the null hypothesis has been rejected when the alternative hypothesis has been true,

the alternative hypothesis is true

In hypothesis testing if the null hypothesis is rejected,

H0: P <= 0.75 Ha: P > 0.75

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

H0: P >= 0.35 Ha: P < 0.35

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

H0: μ ≤ 21.80 Ha: μ > 21.80

The average hourly wage of a computer programmers with 2 years of experience has been $21.80. Because of high demand for computer programmers, it is believed that there has been a significant increase in the average wage of computer programmers. To test whether or not there has been an increase, the correct hypotheses to be tested are:

H0: μ <= 40,000 Ha: μ > 40,000

The average life expectancy of tires produced by the Whitney Tire Company has been 40,000 miles. Management believes that due to a new production process, the life expectancy of their tires has increased. In order to test the validity of their belief, the correct set of hypotheses is

H0: μ≥ 40.1 Ha: μ<40.1

The average manufacturing work week in the metropolitan Chattanooga was 40.1 hours last year. It is believed that the recession has led to a reduction in the average work week. To test the validity if this belief, the hypotheses are:

H0: μ≥ 700 Ha: μ<700

The average rent for a one bedroom apartment in Chattanooga has been $700. Because of the downturn in the real estate market, it is believed that there has been a decrease in the average rental. The correct hypotheses to be tested are:

a Type I error

The error of rejecting a true null hypothesis is

is (1 - confidence level)

The level of significance

rejecting a true null hypothesis

The level of significance in hypothesis testing is the probability of

maximum allowable probability of Type I error

The level of significance is the

H0: μ <= 5 Ha: μ > 5

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

null hypothesis

The p-value is a probability that measures the support (or lack of support) for the

the Level of Significance

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

α

The probability of making a Type I error is denoted by

H0: P <= 0.30 Ha: P > 0.30

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

p-value <= α

When the p-value is used for hypothesis testing, the null hypothesis is rejected if

H0: μ <= 10.0% Ha: μ > 10.0%

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