Stats exam questions | Numerical analysis homework help
P3 – where applicable, readings from tables must be used.
1.
The quality-control manager at a light bulb factory needs to determine whether the mean life of a large shipment of light bulbs is equal to 375 hours. The population standard deviation is 100 hours. A random sample of 64 light bulbs indicates a sample mean life of 350 hours.
a)At the 0.05 level of significance, is there evidence that the mean life is different from 375 hours?
b)Compute the p-value and interpret its meaning.
c)Construct a 95% confidence interval estimate of the pupulation mean life of the light bulbs.
d)Compare the reuslts of (a) and (c). What conclusions do you reach?
2.If, in a sample of n = 16 selected from a normal population, X ̅ = 56 and S = 12, what is the value of tSTAT if you are testing the null hypothesis H0: = 50?
3.In problem 2 above, how many degrees of freedom are there in the t- test?
4.In problems 2 and 3 , what are the critical values of t if the level of significance, α is 0.05 and the alternative hypothesis, H1, is ≠ 50?
5.In problem 2, 3 and 4, what is your statistical decision if the alternative hypothesis, H1 is ≠ 50?
6.In a training process, the average time taken is 6.4 hours. Eight employees were trained using a new method and they had an average training time of 6.2 hours and a standard deviation of 1.1 hours. Use α = 0.01 to determine if the new process reduced the training time.
Question 1
In testing for differences between the means of two related populations, the null hypothesis is
H0 : D = 2.
H0 : D = 0.
H0 : D < 0.
H0 : D > 0.
Question 2
A powerful women’s group has claimed that men and women differ in attitudes about sexual discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem. Find the value of the test statistic.
Z = -2.55
Z = -0.85
Z = -1.05
Z = -1.20
Question 3
When testing H0 : π 1 – π 2 0 versus H1 : π 1 – π 2 > 0, the observed value of the Z-score was found to be -2.13. The p-value for this test would be
0.0166.
0.0332.
0.9668.
0.9834.
Question 4
Given the following information, calculate the degrees of freedom that should be used in the pooled-variance t test.
s12 = 4 s22 = 6
n1 = 16n2 = 25
df = 41
df = 39
df = 16
df = 25
Question 5
TABLE 10-1
Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below.
AmericanJapanese
Sample size211100
Mean SSATL Score65.7579.83
Population Std. Dev.11.076.41
Referring to Table 10-1, give the null and alternative hypotheses to determine if the mean SSATL score of Japanese managers differs from the mean SSATL score of American managers.
H0 : A – J 0 versus H1 : A – J < 0
H0 : A – J 0 versus H1 : A – J > 0
H0 : A – J = 0 versus H1 : A – J ≠ 0
H0 : X ̅ A – X ̅ J 0 versus H1 : X ̅ A – X ̅ J ≠ 0
Question 6
TABLE 10-5
To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below.
StudentExam score
Before Course (1)Exam Score
After course (2)
1530670
2690770
39101000
4700710
5450550
6820870
7820770
8630610
Referring to Table 10-5, what is the critical value for testing at the 5% level of significance whether the business school preparation course is effective in improving exam scores?
2.365
2.145
1.761
1.895
Question 7
The t test for the difference between the means of 2 independent populations assumes that the respective
sample sizes are equal.
sample variances are equal.
populations are approximately normal.
All of these.
Question 8
TABLE 10-4
A real estate company is interested in testing whether, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.
Gotham: X ̅G = 35 months, SG2 = 900 Metropolis: X ̅M = 50 months, SM2 =1050
Referring to Table 10-4, what is the standardized value of the estimate of the mean of the sampling distribution of the difference between sample means?
-8.75
-3.69
-2.33
-1.96
Question 9
TABLE 10-4
A real estate company is interested in testing whether, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.
Gotham: X ̅G = 35 months, SG2 = 900 Metropolis: X ̅M = 50 months, SM2 =1050
Referring to Table 10-4, what is the estimated standard error of the difference between the 2 sample means?
4.06
5.61
8.01
16.00
Question 10
Given the following information, calculate sp2, the pooled sample variance that should be used in the pooled-variance t test.
s12 = 4 s22 = 6
n1 = 16n2 = 25
sp2 = 6.00
sp2 = 5.00
sp2 = 5.23
sp2 = 4.00
Question 11
If we are testing for the difference between the means of 2 related populations with samples of n1 = 20 and n2 = 20, the number of degrees of freedom is equal to
39.
38.
19.
18.
Question 12
In testing for differences between the means of two independent populations, the null hypothesis is:
H0 : 1 – 2 = 2.
H0 : 1 – 2 = 0.
H0 : 1 - 2 > 0.
H0 : 1 – 2 < 2.
Question 13
TABLE 10-5
To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below.
StudentExam score
Before Course (1)Exam Score
After course (2)
1530670
2690770
39101000
4700710
5450550
6820870
7820770
8630610
Referring to Table 10-5, the value of the sample mean difference is ________ if the difference scores reflect the results of the exam after the course minus the results of the exam before the course.
0
50
68
400
Question 14
TABLE 10-1
Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below.
AmericanJapanese
Sample size211100
Mean SSATL Score65.7579.83
Population Std. Dev.11.076.41
Referring to Table 10-1, judging from the way the data were collected, which test would likely be most appropriate to employ?
paired t test
pooled-variance t test for the difference between two means
F test for the ratio of two variances
Z test for the difference between two proportions
Question 15
TABLE 10-3
The use of preservatives by food processors has become a controversial issue. Suppose 2 preservatives are extensively tested and determined safe for use in meats. A processor wants to compare the preservatives for their effects on retarding spoilage. Suppose 15 cuts of fresh meat are treated with preservative I and 15 are treated with preservative II, and the number of hours until spoilage begins is recorded for each of the 30 cuts of meat. The results are summarized in the table below.
Preservative IPreservative II
X ̅I = 106.4 hours X ̅II = 96.54 hours
SI = 10.3 hours SII = 13.4 hours
Referring to Table 10-3, state the null and alternative hypotheses for testing if the population variances differ for preservatives I and II.
H0 : – I2 – II2 0 versus H1 : I2 – II2 < 0
H0 : – I2 – II2 0 versus H1 : I2 – II2 > 0
H0 : – I2 – II2 = 0 versus H1 : I2 – II2 ≠ 0
H0 : – I2 – II2 ≠ 0 versus H1 : I2 – II2 = 0
Question 16
If we are testing for the difference between the means of 2 independent populations presumes equal variances with samples of n1 = 20 and n2 = 20, the number of degrees of freedom is equal to
39.
38.
19.
18.
Question 17
TABLE 10-2
A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. Analysis of the mean salaries of the females and males in the sample is given below.
Hypothesized Difference0
Level of significance0.05
Population 1 Sample
Sample size18
Sample Mean48266.7
Sample Standard Deviation13577.63
Population 2 Sample
Sample Size12
Sample Mean55000
Sample Standard Deviation11741.29
Difference in Sample Means-6733.3
t- Test Statistic-1.40193
Lower-Tail Test
Lower Critical value-1.70113
p-value0.085962
Referring to Table 10-2, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. From the analysis in Table 10-2, the correct test statistic is:
0.0860
-1.4019
-1.7011
-6,733.33
Question 18
TABLE 10-2
A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. Analysis of the mean salaries of the females and males in the sample is given below.
Hypothesized Difference0
Level of significance0.05
Population 1 Sample
Sample size18
Sample Mean48266.7
Sample Standard Deviation13577.63
Population 2 Sample
Sample Size12
Sample Mean55000
Sample Standard Deviation11741.29
Difference in Sample Means-6733.3
t- Test Statistic-1.40193
Lower-Tail Test
Lower Critical value-1.70113
p-value0.085962
Referring to Table 10-2, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. According to the test run, which of the following is an appropriate alternative hypothesis?
H1 : females > males
H1 : females < males
H1 : females ≠ males
H1 : females = males
Question 19
TABLE 10-1
Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below.
AmericanJapanese
Sample size211100
Mean SSATL Score65.7579.83
Population Std. Dev.11.076.41
Referring to Table 10-1, what is the value of the test statistic?
-14.08
-11.8092
-1.9677
96.4471
Question 20
In testing for the differences between the means of 2 independent populations where the variances in each population are unknown but assumed equal, the degrees of freedom are
n – 1.
n1 + n2 – 1.
n1 + n2 – 2.
n – 2.