ST 560 Final

Which of the following has a chi-square distribution?

(n - 1)s2/σ2

The results of a recent poll on the preference of shoppers regarding two products are shown below. Product Shoppers Surveyed Shoppers favoring product A 800 560 B 900 612 The 95% confidence interval estimate for the difference between the populations favoring the products is

-.024 to .064

Read the t statistic from the t distribution table and circle the correct answer. For a one-tailed test (lower tail) with 22 degrees of freedom at α = .05, the value of t =

-1.717

For a two-tailed hypothesis test with a sample size of 20 and a .05 level of significance, the critical values of the test statistic t are ​

-2.093 and 2.093

The following information was obtained from matched samples taken from two populations. Assume the population of differences is normally distributed. Individual: 1,2,3,4,5 Method 1: 7,5,6,7,5 Method 2: 5,9,8,7,6 ​ The 95% confidence interval for the difference between the two population means is

-3.776 to 1.776

A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information. Today Five Years Ago x-bar 82 88 σ2 112.5 54 n 45 36 The point estimate for the difference between the means of the two populations is

-6

In a two-tailed hypothesis test, the test statistic is determined to be z = -2.5. The p-value for this test is

.0124

The results of a recent poll on the preference of shoppers regarding two products are shown below. Product Shoppers Surveyed Shoppers favoring product A 800 560 B 900 612 the standard error of p1-p2 is

.044

Salary information regarding male and female employees of a large company is shown below. Male Female sample size 64 36 Sample mean sal. 44 41 pop variance 128 72 If you are interested in testing whether or not the population average salary of males is significantly greater than that of females, the p-value is

.0668

A sample of 20 cans of tomato juice showed a standard deviation of .4 ounces. A 95% confidence interval estimate of the variance for the population is

.0925 to .3413

A sample of 60 items from population 1 has a sample variance of 8 while a sample of 40 items from population 2 has a sample variance of 10. If we want to test whether the variances of the two populations are equal, the test statistic will have a value of

1.25

Read the t statistic from the t distribution table and circle the correct answer. For a one-tailed test (upper tail) with a sample size of 26 and at the .10 level, t =

1.316

The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card. You are given the following information. Store's Card Major Credit Card Sample size 64 49 sample mean $140 $125 Population stdev. $10 $8 A point estimate for the difference between the mean purchases of all users of the two credit cards is

15

Two major automobile manufacturers have produced compact cars with engines of the same size. We are interested in determining whether or not there is a significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data (in miles per gallon) show the results of the test. Assume the population of differences is normally distributed. Driver: 1,2,3,4,5,6,7,8 Manufacturer A: 32,27,26,25,29,31,25 Manufacturer B: 28,22,27,24,24,25,28,27 The mean of the differences is

2.0

Read the z statistic from the normal distribution table and circle the correct answer. For a two-tailed test using α = .0160, z =

2.41

Based on the sample evidence below, we want to test the hypothesis that population A has a larger variance than population B sample A Sample B n 11 10 s2 12.1 5 The test statistic for this problem equals

2.42

It is known that the population variance (σ2) is 144. At 95% confidence, what sample size should be taken so that the margin of error does not exceed 5?

23

An ANOVA procedure is used for data obtained from four populations. Four samples, each comprised of 30 observations, were taken from the four populations. The numerator and denominator (respectively) degrees of freedom for the critical value of F are

3 and 116

The critical F value with 8 numerator and 29 denominator degrees of freedom at α = .01 is

3.20

From a population with a variance of 900, a sample of 225 items is selected. At 95% confidence, the margin of error is

3.92

We are interested in conducting a study to determine the percentage of voters of a state would vote for the incumbent governor. What is the minimum sample size needed to estimate the population proportion with a margin of error of .05 or less at 95% confidence?

385

An ANOVA procedure is used for data obtained from five populations. Five samples, each comprised of 20 observations, were taken from the five populations. The numerator and denominator (respectively) degrees of freedom for the critical value of F are

4 and 95

The manager of the service department of a local car dealership has noted that the service times of a sample of 30 new automobiles has a standard deviation of 6 minutes. A 95% confidence interval estimate for the standard deviation of the service times (in minutes) for all their new automobiles is

4.778 to 8.066

A random sample of 64 SAT scores of students applying for merit scholarships showed an average of 1400 with a standard deviation of 240. The margin of error at 95% confidence is

59.94

A population has a standard deviation of 50. A random sample of 100 items from this population is selected. The sample mean is determined to be 600. At 95% confidence, the margin of error is

9.8

X^2 .972 = 8.231 indicates that​

97.5% of the chi-square values are greater than 8.231

A 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

H0: p .30 Ha: p < .30

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 40,000 Ha: μ > 40,000

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

H0: μ = 5.8 Ha: μ ≠ 5.8

The bottler of a certain soft drink claims their equipment to be accurate and that the variance of all filled bottles is .05 or less. The null hypothesis in a test to confirm the claim would be written as

H0: σ2 ≤ .05

A random sample of 25 employees of a local company has been taken. A 95% confidence interval estimate for the mean systolic blood pressure for all employees of the company is 123 to 139. Which of the following statements is valid?

If the sampling procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure.

The F ratio in a completely randomized ANOVA is given by

MSTR/MSE

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution

becomes smaller

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

equal to the level of significance

The independent variable of interest in an ANOVA procedure is called a

factor

Regarding inferences about the difference between two population means, the sampling design that uses a pooled sample variance in cases of equal population standard deviations is based on

independent samples

In the hypothesis testing procedure, α is the

level of significance

For the interval estimation of μ when σ is known and the sample is large, the proper distribution to use is the

normal distribution

The sampling distribution p1-bar - p2-bar is approximated by

normal distribution

In an analysis of variance, one estimate of σ2 is based upon the differences between the treatment means and the

overall sample mean

The symbol used for the variance of the sample is

s2

Two major automobile manufacturers have produced compact cars with engines of the same size . We are interested in determining whether or not there is a significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data (in miles per gallon) show the results of the test. Assume the population of differences is normally distributed. Driver Manufacturer A Manufacturer B 1 32 28 2 27 22 3 26 27 4 26 24 5 25 24 6 29 25 7 31 28 8 25 27 ​ At α = .10, the null hypothesis

should be rejected

From a population that is normally distributed, a sample of 25 elements is selected and the standard deviation of the sample is computed. For the interval estimation of μ, the proper distribution to use is the

t distribution with 24 degrees of freedom.

In the analysis of variance procedure (ANOVA), "factor" refers to

the independent variable

In a factorial experiment, if there are x levels of factor A and y levels of factor B, there is a total of ​

xy treatment combinations​.

The symbol used for the variance of the population is

σ2

We are interested in testing to see if the variance of a population is less than 7. The correct null hypothesis is

σ2 ≥ 7.

In order to estimate the average time spent per student on the computer terminals at a local university, data were collected for a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.8 hours. If the sample mean is 9 hours, then the 95% confidence interval is

​8.61 to 9.39 hours

If we are testing for the equality of three population means, we should use the

​test statistic F