AMAT210/ACSC224 Spring 2005. Practice Quiz 3. C.I.'s for the difference of two
means,. Goodness –of-fit test, Chi-square test of independence. Questions 1 ...
AMAT210/ACSC224 Spring 2005
Practice Quiz 3 C.I.’s for the difference of two means, Goodness –of-fit test, Chi-square test of independence Questions 1 and 4 For the variable “Time spent watching TV in Typical Day,” here are results of a twosample t-procedure that compares a random sample of men and women at a college. Sex f m
N 116 59
Mean 1.95 2.37
StDev 1.51 1.87
SE Mean 0.14 0.24
95% CI for mu (f) - mu (m): ( -0.97,
0.14)
1. Using this data, we will create a confidence interval for the parameter A. p1-p2
B. µ
C. x 1 − x 2
D. µ1-µ2
2. The point estimate of the parameter of interest is A. p1-p2 B. µ C. x 1 − x 2 D. µ1-µ2 3. What is the value of the point estimate in this example? B. 2.37 C. –0.97 D. –0.42 A. 1.95 4. What is the standard error of the point estimate in this example? Answer:
Questions 5 to 7 Is there a relationship between the color of one's eyes and the comparative lengths of one's index and ring fingers? Students were asked "which finger is longer: your index finger or your ring finger? Or are they the same?" They also reported the color of their eyes (blue, brown, green, or hazel). The results are given below. Same blue brown green hazel Total
'Index' Longer 5 13 6 5 29
5. The degrees of freedom for this test are: A. 2 B. 3 C. 6 D. 12
'Ring' Longer 26 22 6 16 70
Total 28 58 15 29 130
59 93 27 50 229
AMAT210/ACSC224 Spring 2005
6. The χ2- statistic is smaller than the corresponding critical value for α=5% significance level. One should conclude that: A. There is a statistically significant relationship between eye color and the comparative length of the index and ring fingers. B. There is not a statistically significant relationship between eye color and the comparative length of the index and ring fingers. C. There is insufficient information given because the degrees of freedom of the test statistic are not specified. D. There is a statistically significant relationship between eye color and the comparative length of the index and ring fingers for some eye colors but not for others. 7. The expected count for "blue eyes" and "same" is: A. 59/3 B. 29/4 C. 229/12 D. (59)(29)/229 ________________________________________________________________________ 8. Suppose that a two-way table displaying sample information about gender and opinion about the legalization of marijuana (yes or no) is examined using a chi-square test. The necessary conditions are met and the chi-square value is calculated to be 15. What conclusion can be made? A. Gender and opinion have a statistically significant relationship B. Gender and opinion do not have a statistically significant relationship C. It is impossible to make a conclusion because we don’t know the sample size. D. It is impossible to make a conclusion because we don’t know the degrees of freedom. ______________________________________________________________________
Questions 9 -11 The director of human resources collected the following data on absenteeism by day of the week. Using the chi-square goodness-of-fit test at the 5% level, she wants to test wether there is no difference in the absence rate by day of the week? Day Monday Tuesday Wednesday Thursday Friday
Frequency 124 74 104 98 120
9. The degrees of freedom for this test are: A. 1 B. 7 C. 4 D. 5 10. What is the null hypothesis: There is no difference in the absence rate by day of the week. 11. The expected frequency for any of the days is: 520/5=104
