Stats 3

The average cost of tuition and room and board at a small private liberal arts college is reported to be $8,500 per term. 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

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

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 variance of this sample?

1.386

For a hypothesis comparing two population means, H0: μ1 ≤ μ2, what is the critical value for a one-tailed hypothesis test, using a 5% significance level, with both sample sizes equal to 13? Assume the population standard deviations are equal.

1.711

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

1.711

A large department store examined a sample of the 18 credit card sales and recorded the amounts charged for each of three types of credit cards: MasterCard, Visa, and Discover. Six MasterCard sales, seven Visa, and five Discover sales were recorded. The store used an ANOVA to test if the mean sales for each credit card were equal. What are the degrees of freedom for the F statistic?

2 in the numerator, 15 in the denominator

Below is the information for a completely randomized experimental design involving four treatments, where 12 observations were recorded for each treatment for a total of 48 observations. SST = 210 (Sum of Squares Between Groups). SS Total = 840 (Sum of Squares Total). The computed value of F, or the test statistic, is ______.

4.88

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 The sample mean is 7.557, rounded to 7.6. It is found by summing all the values (52.9) and dividing by the sample size (7).

In an ANOVA problem involving three treatments and 12 observations per treatment, SSE = 297. The MSE for this scenario is ______.

9 The number of treatments, k = 3. The number of total observations, n = 36. The degrees of freedom for the Sum of the Squares-Error, (n − k) = 33. The "Source of Variation-Error", SSE = 297. Therefore, the Mean Square Error, MSE = SSE/(n − k) = 297/33 = 9.

In hypothesis testing, which of the following statements is true concerning the level of significance?

All Apply

If an ANOVA test is conducted and the null hypothesis is rejected, what does this indicate?

At least one pair of population means is different.

Which of the following is used to determine whether or not to reject the null hypothesis?

Decision rule

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. When evaluated using the 5% level of significance, which of the following would be the best decision/interpretation of the null hypothesis?

Fail to reject the null hypothesis.

At the 0.01 significance level, is there a difference in the mean number of times men and women send a Twitter message in a day? Based on the p-value, what is your conclusion?

Fail to reject the null hypothesis.

A p-value is the same as a stated significance level.

False

For a one-tailed test with a .05 level of significance, the critical z statistic is 1.645, while the critical t statistic is 1.96.

False

If we are testing for the difference between two population means and assume that the two populations have equal but unknown standard deviations, the sample standard deviations are pooled to compute the best estimate of the unknown population standard deviation. The result is then squared to arrive at the best estimate of the population variance.

False

In an ANOVA table, k represents the total number of sample observations and n represents the total number of treatments.

False

The alternative hypothesis used in ANOVA is H1: All population means are equal.

False

The average cost of tuition and room and board at a small private liberal arts college is reported to be $8,500 per term. 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

The researcher is interested in determining whether there is evidence that the two processes yield different average errors. The population standard deviations are unknown but are assumed equal. What is the null hypothesis?

H0: µA = µB

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

In both tails

At the 0.01 significance level, what is the conclusion about the way women and men save?

Reject the null hypothesis and conclude that women save more than men.

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.

The researcher is interested in determining whether there is evidence that the two processes yield different average errors. The population standard deviations are unknown but are assumed equal. If we test the null hypothesis at the 1% level of significance, which of the following is the correct decision?

Reject the null hypothesis and conclude the means are different.

A test statistic is a value, determined from sample information, used to decide whether to reject the null hypothesis.

True

An example of a NULL hypothesis is: A person is innocent until proven guilty.

True

For an ANOVA test, rejecting the null hypothesis does not identify which treatment means differ significantly.

True

Hypothesis testing is a procedure based on sample evidence and probability theory to determine whether the hypothesis is a reasonable statement.

True

If the null hypothesis states that there is no difference between the mean net income of retail stores in Chicago and New York City, then the test is two-tailed.

True

The level of significance is the probability of rejecting the null hypothesis when it is actually true.

True

The researcher must decide on the level of significance after setting up the null hypothesis and alternate hypothesis, but before formulating a decision rule and collecting sample data.

True

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.

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 = .05, what is the critical t value?

±2.447 H0: µ = 6.6; H1: µ ≠ 6.6. The t critical values for a two-tailed test at the 0.05 significance level with n − 1, or 6 degrees of freedom are ±2.447.

The researcher is interested in determining whether there is evidence that the two processes yield different average errors. The population standard deviations are unknown but assumed equal. What is the critical t value at the 1% level of significance?

±2.797 The hypothesis test, H0: µA = µB, is based on a t-statistic with degrees of freedom: nA + nB − 2 = 12 + 14 − 2 = 24 . Go to the t table, go down the left-hand column to 24 degrees of freedom, move across that row to the column labeled: two-tailed test at the 0.01 significance level. The value is ±2.797 because it is a two-tailed hypothesis test.

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 Since the critical value is negative, the rejection region is in the lower tail. We could then look in Student's t Distribution (Appendix B.5) at infinite degrees of freedom to find the number closest to 2.33 (which is 2.326) and look up that column in the chart to discover that it corresponds to a .01 level of significance in a one-tailed test. Alternatively, we could consult Appendix B.3 "areas under the normal curve" for z = −2.33, to calculate the area in the tail is 0.5000 − 0.4901 = 0.0099, which rounds to a probability of 0.01.

The researcher is interested in determining whether there is evidence that the two processes yield different average errors. The population standard deviations are unknown but are assumed equal. What is the computed value of t?

−3.299