Posted: January 31st, 2023

Overview of Stats. Questions

Question description

Question 1 of 19
Two samples drawn from two populations are
independent if
 A.  the
selection of one sample from a population is not related to the selection of
the second sample from the same population.  
 B.  the
selection of one sample from one population does not affect the selection of
the second sample from the second population.  
 C.  the
selection of one sample from a population is related to the selection of the
second sample from the same population.  
 D.  two
samples selected from the same population have no relation.  
Question 2 of 19
The mean GPA (grade point average) of all
male students at a college is 2.78 and the mean GPA of all female students at
the same college is 2.98. The standard deviations of the GPAs are .35 for the
males and .36 for the females. Suppose we take one sample of 45 male students
and another sample of 35 female students from this college. Assume the populations
are normally distributed.
What is the mean of the sampling
distribution of the difference between the mean GPAs for males and females?
 A.  .20  
 B.  −.20
 
 C.  2.88
 
 D.  .10  
Question 3 of 19
The mean weekly earnings of all female
workers in a state is $759 and the mean weekly earnings of all male workers in
the same state is $822. The standard deviations of the weekly earnings are $89
for the females and $94 for the males. Suppose we take one sample of 331 female
workers and another sample of 295 male workers from this state.
What is the standard deviation of the
sampling distribution of the difference between the mean weekly earnings for
females and males?
 A. 
$10.36  
 B. 
$53.88  
 C. 
$3.22  
 D. 
$7.34  
Question 4 of 19
A sample of 73 female workers and another
sample of 47 male workers from a state produced mean weekly earnings of $729.51
for the females and $765.40 for the males. Suppose that the standard deviations
of the weekly earnings are $80.00 for the females and $96.51 for the males. The
null hypothesis is that the mean weekly earnings are the same for females and
males, while the alternative hypothesis is that the mean weekly earnings for
females is different from the mean weekly earnings for males.
What are lower and upper limits for the
corresponding 95% confidence interval for the difference between the mean
weekly earnings for all female and male workers in this state?
 A. 
−35.89, 16.91  
 B. 
79.34, 7.56  
 C. 
−69.03, −2.75  
 D. 
−63.62, −8.16  
Question 5 of 19
Referring to Q4,
What is the value of the test statistic?
 A.  2.12
 
 B. 
−2.12  
 C. 
−2.21  
 D. 
−3.59  
Question 6 of 19
Referring to Questions 4-5 :
What is the p-value for this test?
 A. 
.0170  
 B. 
.0136  
 C. 
.0000  
 D. 
.0830  
Question 7 of 19
Referring to Questions 4-6 :
Should you reject or fail to reject the
null hypothesis at the 1% significance level?
 A. 
Reject  
 B.  Fail
to reject  
Question 8 of 19
A sample of 16 from a population produced
a mean of 85.4 and a standard deviation of 14.8. A sample of 18 from another
population produced a mean of 74.9 and a standard deviation of 16.0. Assume
that the two populations are normally distributed and the standard deviations
of the two populations are equal. The null hypothesis is that the two
population means are equal, while the alternative hypothesis is that the mean
of the first population is different than the mean of the second population.
The significance level is 1%.
What is the pooled standard deviation of
the two samples?
 A.  2.73
 
 B.  3.93
 
 C. 
15.92  
 D. 
15.45  
Question 9 of 19
Referring to Q8:
What is the standard deviation of the
sampling distribution of the difference between the means of these two samples?
 A.  5.31
 
 B.  5.47
 
 C.  1.35
 
 D. 
131.32  
Question 10 of 19
Referring to Questions 8-9 ;
What is the value of the test statistic, t
?
 A.  .99  
 B.  5.31
 
 C.  7.12
 
 D.  1.98
 
Question 11 of 19
Referring to Questions 8-10:
Should you reject or fail to reject the
null hypothesis at the 1% significance level?
 A. 
Reject  
 B.  Fail
to reject  
Question 12 of 19
A sample of 20 from a population produced
a mean of 65.0 and a standard deviation of 9.2. A sample of 25 from another
population produced a mean of 59.1 and a standard deviation of 12.2. Assume
that the two populations are normally distributed and the standard deviations
of the two populations are equal. The null hypothesis is that the two
population means are equal, while the alternative hypothesis is that the two
population means are different. The significance level is 5%.
Should you reject or fail to reject the
null hypothesis at the 5% significance level?
 A. 
Reject  
 B.  Fail
to reject  
Question 13 of 19
A city recently launched a neighborhood
watch program to control crime. The following table gives the number of crimes
reported in six neighborhoods during the six months before and six months after
the city launched the neighborhood watch program.

Before

After

57

41

73

65

53

28

82

73

79

61

39

32

Let the paired difference be the number of
crimes before minus the number of crimes after the city launched the
neighborhood watch program. The null hypothesis is that the mean of the
population paired differences is equal to zero (i.e. the neighborhood watch
program does not affect the number of crimes.) The alternative hypothesis is
that the mean of the population paired differences is different than zero
(i.e., the neighborhood watch program decreases the number of crimes). The
significance level is 1%.
What is the mean of the sample paired
differences?
 A. 
68.30  
 B. 
13.83  
 C. 
16.60  
 D. 
11.86  
Question 14 of 19
Referring to Question 13:
What is the standard deviation of the
paired differences?
 A. 
22.571  
 B. 
33.88  
 C. 
7.083  
 D. 
5.821  
Question 15 of 19
Referring to questions 13-14:
What is the standard deviation of the mean
of the sample paired differences?
 A. 
3.166  
 B. 
1.181  
 C. 
2.376  
 D. 
2.892  
Question 16 of 19
Referring to Questions 13-15
Calculate the 99% confidence interval for
the mean of the population paired differences that corresponds to these data.
 A. 
3.11, 24.55  
 B. 
4.75, 22.92  
 C. 
4.10, 23.56  
 D. 
2.17, 25.49  
Question 17 of 19
Referring to questions 13-16:
What are the critical values of t for the
hypothesis test?
 A. 
−3.143 and 3.143  
 B. 
−3.365 and 3.365  
 C. 
−3.747 and 3.747  
 D. 
−4.032 and 4.032  
Question 18 of 19
Referring to questions 13-17 :
What is the value of the test statistic, t
 A.  3.67
 
 B.  4.78
 
 C.  9.77
 
 D. 
11.72  
Question 19 of 19
Referring to questions 13-18 :
Should you reject or fail to reject the
null hypothesis?
 A. 
Reject  
 B.  Fail
to reject

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