# Statistics

1) If the correlation coefficient r is equal to 0.57, find the coefficient of determination.

a) 0.68

b) 0.75

c) 0.45

d) 0.32

2) The prediction interval around y' for a specific x is

a) A confidence interval for the true mean value of the y values that correspond to that x

b) The value of y used to calculate the slope of the regression line

c) The interval of values of x used to predict y'

d) The difference between the value of y and the value of x

3) What is the critical t-value for a right-tailed test when a=0.025 and d.f. = 12?

a) 2.179

b) 2.831

c) 2.228

d) 1.869

4) A portion of an ANOVA summary table is shown below.

Source sum of squares degrees of freedom

Between 22 2

Within(error) 39 34

Total 61

a) dfN = 2, dfD = 34

b) dfN = 34, dfD = 2

c) dfN = 22, dfD = 39

d) dfN = 39, dfD = 22

5) If r = -0.726 and n = 6, test the significance of the correlation coefficient at a = .05

a) Reject p=0 because 2.91 > 2.57

b) Do not reject p=0 because -2.11 < 2.57

c) Do not reject p=0 because -2.11 < 2.54

d) Do not reject p=0 because 2.91 < 2.54

6) Use a P- value to test the claim about the population mean, m # 230; using the given sample statistics. State your decision for alpha = 0.05

Claim: m # 230; Sample statistics: x (bar) = 216.5, s = 17.3, n = 48

7) Use a t-test to investigate the claim and assume that the population is normally distributed:

A large university says the mean number of classroom hours per week for full-time faculty is more than 9. A random sample of the number of classroom hours for full-time faculty for one week is listed. At alpha = 0.05, test the university's claim.

10.7 9.8 11.6 9.7 7.6 11.3 14.1 8.1 11.5 8.5 6.9

#### Solution Summary

This solution is comprised of detailed step-by-step calculations and analysis of the given problems related to Statistics and provides students with a clear perspective of the underlying concepts. The hypothesis tests have also been shown in interactive EXCEL sheets for better understanding of the steps and calculations.