30 Jul 23 MCQs In Statistics …
1.A one-way ANOVA is to be performed to test the null hypothesis that several populations have the same mean. Compute the value of the F test statistic for this hypothesis test.
Given the sample data below, find the value of the F test statistic for a test of the claim that the populations have the same mean.
Brand A Brand B Brand C
n = 12 n = 12 n = 12
x-bar = 6.33 x-bar = 5.82 x-bar = 7.37
S2 = 1.25 S2 = 1.53 S2 = 1.77
a.F = 4.937
b. F = 3.621
c. F = 2.304
d. F = 6.254
2. Compute the sum of squares.
A one-way ANOVA is to be performed. Independent random samples are selected from three different populations. The sample data are given in the table below.
A B C
4 2 5
7 1 8
7 8
3
Compute the total sum of squares, SST
A. 1800
B. 56.0
C. 281.0
D 256.0
3. True or False.
A one-way ANOVA is to be performed. The error mean square gives a measure of the variation within the samples, while the treatment mean square gives a measure of variation among the sample means.
4. True or false? A one-way ANOVA test can be right-tailed, left-tailed, or two-tailed
depending on the alternative hypothesis
5. True or False? In a one-way ANOVA, the null hypothesis will be rejected if the variation among the sample means is large relative to the variation within the samples.
6. True of False? A one-way ANOVA is being performed. True or false? The null hypothesis will be rejected if SSE is large relative to SSTR.
7. When performing a hypothesis test for the population linear correlation coefficient, ρ, the test statisitic is t = r/√[(1 – r2)/(n – 2)]What is the distribution of this test statistic if the null hypothesis, H0: ρ = 0 is true?
A. chi-square distribution with df = n – 2
B. t-distribution with df = n – 2
C. normal distribution
D. t-distribution with df = n – 1
8. True or false? When performing regression analysis, different samples will all yield the same sample regression line.
9.True or false? In the regression model, if β1= 0, then for each value x of the predictor variable, the conditional distribution of the response variable is a normal distribution with a mean which is independent of x.
10. Compute the sum of squares.
A one-way ANOVA is to be performed. Independent random samples are selected from three different populations. The sample data are given in the table below.
A B C
7 5 2
5 2 6
9 4
5
Compute the total sum of squares, SST.
a. 40.0
b. 243.7
c. 86.4
d. 18.7
11. True or false? In the context of regression analysis, the sum of the residuals is always zero.
12. Obtain the required prediction interval. You may presume that the assumptions for regression inferences are met.
Ten students in a graduate program were randomly selected. Their grade point averages (GPAs) when they entered the program were between 3.5 and 4.0. The following data consist of the students’ GPAs on entering the program and their current GPAs.
Entering GPA, x Current GPA, y
3.5 3.6
3.8 3.7
3.6 3.9
3.6 3.6
3.5 3.9
3.9 3.8
4.0 3.7
3.9 3.9
3.5 3.8
3.7 4.0
The equation of the regression line is ŷ = 3.67 + 0.0313x. The standard error of the estimate is approximately 0.14521. Determine a 99% prediction interval for the current GPA of a student with an entering GPA of 3.5.
a. 3.24 to 4.32
b. 3.55 to 4.01
c. 3.31 to 4.24
d. 3.27 to 4.29
13.
A one-way ANOVA is to be performed to test the null hypothesis that several populations have the same mean. Compute the value of the F test statistic for this hypothesis test.
Given the sample data below, find the value of the F test statistic for a test of the claim that the populations have the same mean.
Brand A Brand B Brand C Brand D
n = 51 n = 51 n = 51 n = 51
x-bar = 25.1 x-bar = 22.8 x-bar = 23.1 x-bar = 24.5
s = 3.01 s = 2.76 s = 4.06 s = 3.85
A.F = 16.253
B. F = 4.688
C. F = 5.169
D. F = 17.921
14. A one-way ANOVA is performed to compare the means of three populations. The sample sizes are 8, 12, and 13. Determine the degrees of freedom for the F-statistic.
A. (2, 30)
B. (2, 32)
C. ( 30, 32)
D. (3, 30)
15. In the context of regression analysis, which of the following, roughly speaking , does the standard error of the estimate give an indication of?
A. How much, on average, the predicted values of the response variable differ from the observed values of the response variable.
B. How much, on average, the values of the response variable differ from their mean.
C. How much, on average, the values of the predictor variable differ from their mean.
D. How much the slope of the sample regression line differs from the slope of the population regression line.
16. True or false? In the context of regression, the term confidence is usually reserved for interval estimates of parameters while the term prediction is used for interval estimates of variables.
17. True or false? In the regression model, the predictor variable is useful in predicting the response variable provided that β1 = 0.
18. True or false? In a one-way ANOVA, if the null hypothesis is rejected, we conclude that the population means are all different (i.e., no two of the population means are equal).
19.
Perform the required correlation test. You may presume that the assumptions for regression inferences are met.
A grass seed company conducts a study to determine the relationship between the density of seeds planted (in pounds per 500 sq ft) and the quality of the resulting lawn. Eight similar plots of land are selected and each is planted with a particular density of seed. One month later the quality of each lawn is rated on a scale of 0 to 100. The sample data are given below.
Seed Density, x Lawn Quality, y
1 30
1 40
2 40
3 40
3 50
3 65
4 50
5 50
Using technology, determine whether the data provide sufficient evidence to conclude that seed density and lawn quality are positively linearly correlated. Test at the 1% significance level using the hypotheses H0: ρ = 0, Ha: ρ > 0 .
a. Test statistic: t = 0.77778
Critical value: t = 3.143
Do not reject H0. At the 1% significance level, the data do not provide sufficient evidence to conclude that seed density and lawn quality are positively linearly correlated.
b.. Test statistic: t = 1.8372
Critical value: t = 3.143
Do not reject H0. At the 1% significance level, the data do not provide sufficient evidence to conclude that seed density and lawn quality are positively linearly correlated.
c. Test statistic: t = 0.1004
Critical value: t = 3.143
Do not reject H0. At the 1% significance level, the data do not provide sufficient evidence to conclude that seed density and lawn quality are positively linearly correlated.
d. Test statistic: t = 12.472
Critical value: t = 3.143
Reject H0. At the 1% significance level, the data provide sufficient evidence to conclude that seed density and lawn quality are positively linearly correlated.
20. In a study of the relationship between weight and height, a sample regression equation is obtained, in which height is used as the predictor variable. This sample regression equation is then used to make inferences.
True or false? The point estimate of the mean weight of all subjects of height 65 inches will be equal to the predicted weight of an individual of height 65 inches.
21. Obtain the required confidence interval for the slope of the population regression line. You may presume that the assumptions for regression inferences are met.
A set of sample data consisting of 22 pairs of x and y values yields a regression equation of y = 5.93 + 0.19x. The standard error of the estimate is approximately 13.24 and Sxx = 51,657. Obtain a 95% confidence interval for the slope of the population regression line that relates y to x.
A.0.07 to 0.31
B. 5.81 to 6.05
C. 0.04 to 0.34
D. 0.09 to 0.29
22. True or false? When performing a one-way ANOVA, the error sum of squares can be obtained by subtracting the treatment sum of squares from the total sum of squares.
23. True or false? The sample linear correlation coefficient, r, measures the linear correlation of all possible pairs of observations of the two variables
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