Question 1

In a television commercial, the manufacturer of a toothpaste claims that at least 4 out of 5 dentists recommend its product. A consumer-protection group wants to test that claim. Identify the hypotheses.

Accepted Answer

The answer of In a television commercial, the manufacturer of...

Question 2

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 sample information reported below, carry out a test of this statement. Use a .05 level of significance.

Accepted Answer

The answer of An official of a large national union...

Question 3

You are given the following information obtained from a random sample of 5 observations.
  At a 10% level of significance, use Excel to determine whether or not the mean of the population from which this sample was taken is significantly less than 21. (Assume the population is normally distributed.)

Accepted Answer

The answer of You are given the following information obtained...

Question 4

Fast 'n Clean operates 12 laundromats on the east side of the city. All of Fast 'n Clean's clothes dryers have a label stating "20 minutes for $1.00." You question the accuracy of the dryers' clocks and decide to conduct an observational study. You randomly select 36 dryers in several different Fast 'n Clean locations, put $1.00 in each and time the drying cycle. The sample mean drying time is 20 minutes and 25 seconds. The manufacturer of the dryer states that the standard deviation for 20-minute drying cycles is 1 minute.
a. Using the sample data and $\alpha$= .05, test the validity of the label on the dryers. Apply the p-value and critical value approaches to conducting the two-tail hypothesis test.
b. Conduct the same two-tail hypothesis test, but this time use the confidence interval approach to hypothesis testing.

Accepted Answer

The answer of Fast 'n Clean operates 12 laundromats on...

Question 5

For each shipment of parts a manufacturer wants to accept only those shipments with at most 10% defective parts. A large shipment has just arrived. A quality control manager randomly selects 50 of the parts from the shipment and finds that 6 parts are defective. Is this sufficient evidence to reject the entire shipment? Use a .05 level of significance to conduct the appropriate hypothesis test.

Accepted Answer

The answer of For each shipment of parts a manufacturer...

Question 6

You are given the following information obtained from a random sample of 4 observations.
  At a .05 level of significance, use Excel 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.)

Accepted Answer

The answer of You are given the following information obtained...

Question 7

A national poll reported that 58% of those with Internet access have made purchases online. To investigate whether this percentage applies to its own state, a legislator commissions a study. A random sample of 400 state residents who have Internet access is taken. Of those 400 respondents, 215 said that they have made purchases online. Does this sample provide sufficient evidence to conclude that the state differs from the nation with respect to making purchases online? Use the p-value to conduct the hypothesis test and use a .05 level of significance.

Accepted Answer

The answer of A national poll reported that 58% of...

Question 8

The board of directors of a corporation has agreed to allow the human resources manager to move to the next step in planning day care service for employees' children if the manager can prove that at least 25% of the employees have interest in using the service. The HR manager polls 300 employees and 90 say they would seriously consider utilizing the service. At the $\alpha$ = .10 level of significance, is there enough interest in the service to move to the next planning step?

Accepted Answer

The answer of The board of directors of a corporation...

Question 9

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 more than $45,000. A random sample of 9 households showed the following results.
  Use the statistical techniques in Excel to advise the group on whether or not they should locate the boutique in this store. Use a .05 level of significance. (Assume the population is normally distributed.)

Accepted Answer

The answer of A group of young businesswomen wish to...

Question 10

A manufacturer is considering a new production method. The current method produces 94% non-defective (good) parts. The new method will be implemented if it produces more non-defectives than the current method. Identify the hypotheses.

Accepted Answer

The answer of A manufacturer is considering a new production...

Question 11

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 distribution of the population is normally distributed.
  
a.State the null and alternative hypotheses.
b.Using a critical value, test the hypothesis at the 10% level of significance.
c.Using a p-value, test the hypothesis at the 10% level of significance.
d.Using a confidence interval, test the hypothesis at the 10% level of significance.
e.Could a Type II error have been committed in this hypothesis test?

Accepted Answer

The answer of Nancy believes that the average running time...

Question 12

Several years ago the proportion of Americans aged 18 - 24 who invested in the stock market was 0.20. A random sample of 25 Americans in this age group was recently taken. They were asked whether or not they invested in the stock market. The results follow:
  At a .05 level of significance, use Excel to determine whether or not the proportion of Americans 18 - 24 years old that invest in the stock market has changed.

Accepted Answer

The answer of Several years ago the proportion of Americans...

Question 13

Identify the null and alternative hypotheses for the following problems.
a.The manager of a restaurant believes that it takes a customer no more than 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.

Accepted Answer

The answer of Identify the null and alternative hypotheses for...

Question 14

A manufacturer claims that at least 40% of its customers use coupons. A study of 25 customers is undertaken to test that claim. The results of the study follow.
  At a .05 level of significance, use Excel to test the manufacturer's claim.

Accepted Answer

The answer of A manufacturer claims that at least 40%...

Question 15

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.Using $\alpha$= 0.05, what is the rejection rule? b.Determine the standard error of the proportion. c.Compute the value of the test statistic z. What is your conclusion? d.Determine the p-value.

Accepted Answer

The answer of Consider the following hypothesis test: H_o: p =0.5 H_a:...

Question 16

A new soft drink is being market tested. A sample of 400 individuals participated in the taste test and 80 indicated they like the taste.
a.At a 5% significance level, test to determine if at least 22% of the population will like the new soft drink.
b.Determine the p-value.

Accepted Answer

The answer of A new soft drink is being market...

Question 17

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 a critical value, test the hypothesis at the 1% level of significance.
c.Using a p-value, test the hypothesis at the 1% level of significance.

Accepted Answer

The answer of A student believes that no more than...

Quiz 9: Hypothesis Tests

In a television commercial, the manufacturer of a toothpaste claims that at least 4 out of 5 dentists recommend its product. A consumer-protection group wants to test that claim. Identify the hypotheses.

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 sample information reported below, carry out a test of this statement. Use a .05 level of significance.

You are given the following information obtained from a random sample of 5 observations. At a 10% level of significance, use Excel to determine whether or not the mean of the population from which this sample was taken is significantly less than 21. (Assume the population is normally distributed.)

A manufacturer is considering a new production method. The current method produces 94% non-defective (good) parts. The new method will be implemented if it produces more non-defectives than the current method. Identify the hypotheses.

A manufacturer claims that at least 40% of its customers use coupons. A study of 25 customers is undertaken to test that claim. The results of the study follow. At a .05 level of significance, use Excel to test the manufacturer's claim.

A new soft drink is being market tested. A sample of 400 individuals participated in the taste test and 80 indicated they like the taste. a.At a 5% significance level, test to determine if at least 22% of the population will like the new soft drink. b.Determine the p-value.