business stats test 3 chap 10

In hypothesis testing, what is the level of significance?

all apply.

Consider a two-tailed test with a level of confidence of 99%. The p-value is determined to be 0.05. Therefore, the null hypothesis ________.

should not be rejected

The average cost of tuition plus room and board at a small private liberal arts college is reported to be $8,500 per term, but a financial administrator believes that the average cost is higher. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745. The population standard deviation is $1,200. Let α = 0.05. What is the critical z value for this test?

+1.645

Consider a right-tailed test (upper tail) and a sample size of 40 at the 95% confidence level. The value of t is ________.

+1.685

The average cost of tuition plus room and board at a small private liberal arts college is reported to be $8,500 per term, but a financial administrator believes that the average cost is higher. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745. The population standard deviation is $1,200. Let α = 0.05. What is the test statistic for this test?

+3.82

Consider a left-tailed test, where the p-value is found to be 0.10. If the sample size n for this test is 49, then the t statistic will have a value of ________.

-1.299

What is the probability of making a Type II error if the null hypothesis is actually true?

0

The average cost of tuition plus room and board at small private liberal arts colleges is reported to be $8,500 per term, but a financial administrator believes that the average cost is higher. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745. The population standard deviation is $1,200. Let α = 0.05. What is the p-value for this test?

0.0000

Based on the Nielsen ratings, the local CBS affiliate claims its 11 p.m. newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is the p-value?

0.1539

It is claimed that in a bushel of peaches, less than 10% are defective. A sample of 400 peaches is examined and 50 are found to be defective. What is the p-value?

0.9525

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. What is the sample standard deviation?

1.177

Consider a two-tailed test with a level of confidence of 80.30%. The z-value is ________.

1.29

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. What is the sample variance?

1.385

Using a 5% level of significance and a sample size of 25, what is the critical t value for a null hypothesis, H0: µµ ≤ 100?

1.711

If the critical z value for a hypothesis test equals 2.45, what value of the test statistic would provide the least chance of making a Type I error?

10,000

Sales at a fast-food restaurant average $6,000 per day. The restaurant decided to introduce an advertising campaign to increase daily sales. In order to determine the effectiveness of the advertising campaign a sample of 49 days of sales were taken. They found that the average daily sales were $6,400 per day. From past history, the restaurant knew that its population standard deviation is about $1,000. The value of the test statistic is _______.

2.8

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. What are the degrees of freedom?

6

A machine is set to fill the small-size packages of M&M candies with 56 candies per bag. A sample revealed: three bags of 56, two bags of 57, one bag of 55, and two bags of 58. To test the hypothesis that the mean candies per bag is 56, how many degrees of freedom are there?

7

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. What is the sample mean?

7.6

What are the critical values for a two-tailed test with a 0.01 level of significance when n is large and the population standard deviation is known?

Above 2.576 and below -2.576

A random sample of size 15 is selected from a normal population. The population standard deviation is unknown. Assume the null hypothesis indicates a two-tailed test and the researcher decided to use the 0.10 significance level. For what values of t will the null hypothesis not be rejected?

Between -1.761 and 1.761

What statement do we make that determines if the null hypothesis is rejected?

Decision rule

The mean annual income of certified welders is normally distributed with a mean of $50,000 and a population standard deviation of $2,000. The ship building association wishes to find out whether their welders earn more or less than $50,000 annually. The alternate hypothesis is that the mean is not $50,000. If the level of significance is 0.10, what is the decision rule?

Do not reject the null hypothesis if computed z lies between -1.645 and +1.645; otherwise, reject it.

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. What is the decision for a statistical significant change in average weights at birth at the 5% level of significance?

Fail to reject the null hypothesis.

What is a Type II error?

Failing to reject a false null hypothesis

The average cost of tuition plus room and board at small private liberal arts colleges is reported to be $8,500 per term, but a financial administrator believes that the average cost is higher. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745. The population standard deviation is $1,200. Let α = 0.05. Based on the computed test statistic or p-value, what is our decision about the average cost?

Greater than $8,500

For a two-tailed test with a 0.05 significance level, where is the rejection region when n is large and the population standard deviation is known?

Greater than +1.960 and less than -1.960

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. The null hypothesis is ______.

H0: µ = 6.6

The average cost of tuition and room and board at a small private liberal arts college is reported to be $8,500 per term, but a financial administrator believes that the average cost is higher. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745. The population standard deviation is $1,200. Let α = 0.05. What are the null and alternative hypotheses for this study?

H0: µ ≤ $8,500; H1: µ > $8,500

The mean annual incomes of certified welders are normally distributed with the mean of $50,000 and a standard deviation of $2,000. The ship building association wishes to find out whether their welders earn more or less than $50,000 annually. The alternate hypothesis is that the mean is not $50,000. Which of the following is the alternate hypothesis?

H1: µ ≠ $50,000

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. What is the alternate hypothesis?

H1: µ ≠ 6.6

If the alternate hypothesis states that µ ≠ 4,000, where is the rejection region for the hypothesis test?

In both tails

For an alternative hypothesis: µ > 6,700, where is the rejection region for the hypothesis test located?

In the right or upper tail

Define the level of significance.

It is the probability of a Type I error.

A null hypothesis makes a claim about a __________.

Population parameter

For a null hypothesis, H0: µ = 4,000, if the 1% level of significance is used and the z-test statistic is +6.00, what is our decision regarding the null hypothesis?

Reject H0.

The mean weight of newborn infants at a community hospital is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. Does the sample data show a significant increase in the average birthrate at a 5% level of significance?

Reject the null hypothesis and conclude the mean is greater than 6.6 lb.

A consumer products company wants to increase the absorption capacity of a sponge. Based on past data, the average sponge could absorb 3.5 ounces. After the redesign, the absorption amounts of a sample of sponges were (in ounces): 4.1, 3.7, 3.3, 3.5, 3.8, 3.9, 3.6, 3.8, 4.0, and 3.9. At the 0.01 level of significance, what is the decision rule to test if the new design increased the absorption of the sponge?

Reject the null hypothesis if computed t is greater than 2.821.

If we reject the null hypothesis, what can we conclude subject to the probability, α?

Reject the null with a probability, α, of making a Type I error.

What is another name for the alternate hypothesis?

Research hypothesis

Which of the following is NOT one of the six steps in the hypothesis testing procedure?

Select a level for β

To conduct a test of hypothesis with a small sample, we make an assumption that __________.

The population is normally distributed

A manufacturer wants to increase the shelf life of a line of cake mixes. Past records indicate that the average shelf life of the mix is 216 days. After a revised mix has been developed, a sample of nine boxes of cake mix gave these shelf lives (in days): 215, 217, 218, 219, 216, 217, 217, 218, and 218. Using α = 0.025, has the shelf life of the cake mix increased?

Yes, because computed t is greater than the critical value.

The mean length of a candy bar is 43 millimeters. There is concern that the settings of the machine cutting the bars have changed. Test the claim at the 0.02 level that there has been no change in the mean length. The alternate hypothesis is that there has been a change. Twelve bars (n = 12) were selected at random and their lengths recorded. The lengths are (in millimeters) 42, 39, 42, 45, 43, 40, 39, 41, 40, 42, 43, and 42. The mean of the sample is 41.5 and the standard deviation is 1.784. Computed t = -2.913. Has there been a statistically significant change in the mean length of the bars?

Yes, because the computed t lies in the rejection region.

The probability of a Type II error is directly related to ________.

the difference between the hypothesized mean and the sample mean

Which symbol represents a test statistic used to test a hypothesis about a population mean?

z

The mean annual incomes of certified welders are normally distributed with the mean of $50,000 and a standard deviation of $2,000. The ship building association wishes to find out whether their welders earn more or less than $50,000 annually. The alternate hypothesis is that the mean is not $50,000. If the level of significance is 0.10, what is the critical value?

±1.645

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. If α = 0.05, what is the critical t value?

±2.447

What are the critical z-values for a two-tailed hypothesis test if α = 0.01?

±2.576

For a one-tailed hypothesis test, the critical z value of the test statistic is -2.33. Which of the following is true about the hypothesis test?

α = 0.01 for a lower-tailed test

The probability of a Type II error is represented by ________.

β