exam three

A regression analysis between sales (in $1000s) and price (in dollars) resulted in the following equation: y = 50,000 − 8x The above equation implies that an increase of _____.

$1 in price is associated with a decrease of $8,000 in sales

Regression analysis was applied between sales (in $1000s) and advertising (in $100s), and the following regression function was obtained. = 500 + 4x Based on the above estimated regression line, if advertising is $10,000, then the point estimate for sales (in dollars) is _____.

$900,000

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. Final examination scores from a random sample of students enrolled today and from a random sample of students enrolled five years ago were selected. You are given the following information. Today Five Years Ago 82 88 σ 2 112.5 54 n 45 36 Refer to Exhibit 10-3. The test statistic for the difference between the two population means is _____.

-3

In a regression analysis, if SST = 4500 and SSE = 1575, then the coefficient of determination is _____.

.65

Salary information regarding two independent random samples of male and female employees of a large company is . Page 6 shown below. Male Female Sample size 41 35 Sample mean salary (in $1000s) 47 44 Sample variance 115 106 20. Refer to Exhibit 10-1A. The point estimate of the difference between the means of the two populations (Male - Female) is _____.

3

An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below. Under Age 18 Over Age 18 n1 = 500 n2 = 600 Number of accidents = 180 Number of accidents = 150 We are interested in determining if the accident proportions differ between the two age groups. Refer to Exhibit 10-11. The value of the test statistic is _____.

3.96

The following is part of an ANOVA table, which was the result of three treatments and a total of 15 observations. Source of Variation Sum of Squares Degrees of Freedom Mean Square F Between treatments 64 Within treatments (Error) 96 Total 23. Refer to Exhibit 13-7. The mean square between treatments (MSTR) is _____.

32

SSTR = 6,750 H0: μ1 = μ2 = μ3 = μ4 SSE = 8,000 Ha: At least one mean is different nT = 20 25. Refer to Exhibit 13-1. The mean square within treatments (MSE) equals _____.

500

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 ≥ 85 vs Ha: μ < 85

The F ratio in a completely randomized ANOVA is the ratio of _____.

MSTR/MSE

In a regression analysis, if r 2 = 1, then _____.

SSE must be equal to 0

if a hypothesis test leads to the rejection of the null hypothesis, a _____.

Type I error may have been committed

The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is called _____.

a residual

A Type II error is committed when _____.

a true alternative hypothesis is mistakenly rejected

in a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments. The following information is provided. SSTR = 200 (Sum Square Between Treatments) SST = 800 (Total Sum Square) Refer to Exhibit 13-4. The conclusion of the test is that the five means _____.

are not equal

An experimental design where the experimental units are randomly assigned to the treatments is known as _____.

completely randomized design

An example of statistical inference is _____.

hypothesis testing

The rejection region for a one-tailed hypothesis test _____.

is in the tail that supports the alternative hypothesis

Part of an ANOVA table is shown below. Source of Variation Sum of Squares Degrees of Freedom Mean Square F Between treatments 180 3 Within treatments (Error) Total 480 18 Refer to Exhibit 13-5. The conclusion of the test is that the means _____.

may be equal

If the coefficient of correlation is a positive value, then the slope of the regression line _____.

must also be positive

Refer to Exhibit 10-11 and let pu represent the proportion under and po the proportion over the age of 18. The null hypothesis is _____.

pu - po = 0

In order to determine whether or not there is a significant difference between the hourly wages of two companies, two independent random samples were selected and the following statistics were calculated. Company A Company B Sample size 80 60 Sample mean $6.75 $6.25 Population standard deviation $1.00 $0.95 Refer to Exhibit 10-8. The null hypothesis _____.

should be rejected

Independent simple random samples are selected to test the difference between the means of two populations whose variances are not known. The sample sizes are n1 = 32 and n2 = 40. The correct distribution to use is the _____ distribution.

t

Fast 'n Clean operates 16 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 31 dryers in several different Fast 'n Clean locations, put $1.00 in each and time the drying cycle. The sample mean drying time is 19.488 minutes with a standard deviation of 0.9. Assume the distribution of the population is normal. Use a 0.1 level of sig

t = -3.1674 ; reject the null hypothesis

"D" size batteries produced by MNM Corporation have had a life expectancy of 85.8 hours. Because of an improved production process, the company believes that there has been an INCREASE in the life expectancy of its D size batteries. A sample of 54 batteries showed an average life of 88.7 hours with a standard deviation of 3.8 hours. Conduct an appropriate hypothesis test. Find the t-statistic and the appropriate conclusion at the 0.1 level of significance.

t = 5.608 ; reject the null hypothesis