AMS 110 Pretest D Assignment
Question # 00034587
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Updated on: 12/04/2014 12:01 AM Due on: 12/04/2014
SHOW ALL WORK, ENTER ANSWERS ON THE BLANK PROVIDED
Name
SB ID #:_
_ Your TA
This is worth 5% of your final exam grade. Please print and hand in this original document with your work on
it. Show all work in any blank space provided on each page and enter your final answer on the blank line
provided. You may check your work with a calculator, but all computations must be shown.
1. (14 points) A school administrator wants to compare two reading methods: Method S and
method B. A class of 44 students is randomly divided into two groups of 22 each. One is taught
with method S and the other is taught with B. Is the mean reading score with S higher than with
B? The sample mean reading score for method S was 43.0691, with a standard deviation of
5.5641 and the sample mean reading score for method B was 40.0768 with a standard
deviation of 5.2247. These are sample standard deviations. No alpha is provided for this
problem.
State the null and the alternate hypotheses Ho:
versus Ha: ____________
Assume that the data are independent samples from normal populations with equal population
variances. Thus, we perform a pooled variance t test.
Find an estimate of the pooled variance. ______________
(4 decimal places)
Find sp (3 decimals) ____________________
Degrees of Freedom = ______________
The critical value(s) from the t table at the appropriate degrees of freedom are given by
____________________
The t test statistic is ______________
Estimate the p-value______________
State and interpret your decision:
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
Previously, you were asked to perform a pooled variance t-test.
Were we justified in assuming equal variances? To answer this question please conduct a
hypothesis test (F test) to check for equality of variances.
State the null and alternate hypotheses
Ho: ___________________versus Ha: ______________________
State the F test statistic _________________________
The numerator and denominator degrees of freedom______,_____
State the critical value obtained from the F table ____________
(F table is posted under Lectures on Blackboard for your convenience.)
State your conclusion of this F test. Were we justified in conducting a
pooled variance t test?
_______________________________________________________
___________________________________________________(Yes/NO)
If the pooled variance t test is not warranted, (i.e. if variances are not the same), what test is one
supposed to use to compare the means?
______________________________________________________________
TOTAL POINTS FOR #1________
2. (11 points) David wants to compute whether an alternate route to work would be quicker. For the
next 58 working days he randomly divides his observations into two groups of 29 days each.
He drives the first route for one set of 29 days and drives the second for the other set of 29
days recording, for each day, the commuting times in minutes. Assume that times of
commute are normal.
Route 1
n=29
sample mean = 31.945
s=5.87
Route 2
n=29
sample mean = 28.105
s=6.24
a.
Does the assumption of common population standard deviation seem plausible?
State the null and alternate hypotheses Ho:
b.
versus
Ha:_____________
The numerator and denominator degrees of freedom______,______
c.Give the test statistic_________________
d.
What is your decision regarding common variance
___________________________________________________________________
___________________________________________________________________
e.
State the hypothesis to test if route two is quicker than route one.
Ho:
Ha:_________________________
f. The test statistic is ____
g. The p-value is
h. The degrees of freedom are_______________
i. The decision is __________________________________________________________
Route 2 (does/does not) appear to be quicker.
j. State the F critical value from the F table that was used in part d____________
k.State the pooled variance__________________
TOTAL POINTS FOR #2________
3. (13 points) We would like to compare the characteristics of tuberculosis meningitis in patients
infected with HIV and those who are not infected. In particular, we would like to determine whether
the two populations have the same mean age. A sample of 37 infected patients has mean age 27.9
years and a standard deviation 5.6 years. A sample of 19 patients who are not infected has mean
age 38.8 years and standard deviation 21.7 years. Alpha = .05
Conduct a hypothesis test to check for equality of variances.
State the null and alternate hypotheses
Ho___________________versus Ha:__________
Compute the F test statistic ___________
State the numerator and denominator deg of freedom______,_____
State the critical value obtained from the F table ____________
State your conclusion regarding the variances.
_______________________________________________________
_______________________________________________________
_______________________________________________________
Based on (a), what test will you use to determine if the 2 populations have the same mean
age?
_______________________________________________________
We continue with the test on the next page:
State Ho: ______________________ versus
Ha: ______________________
Find the test statistic __________________
State the degrees of freedom (Welch/Satterthwaite)_____________
State the critical value(s) _____________
State your conclusion, and justify your conclusion using the critical values and the test statistic.
_______________________________________________________
_______________________________________________________
_______________________________________________________
Approximate the P-value for this test. ______________________
State the confidence interval for the difference in means________,________
TOTAL POINTS FOR #3________
4. (18 points) Company officials were concerned about the length of time a particular drug product
retained its potency. A random sample of n1 = 10 bottles of the product was drawn from the
production line and analyzed for potency. A second sample of n2 = 10 bottles was obtained and
stored in a regulated environment for 1 year. Let 1 denote the mean potency for all bottles
coming off the production line and let 2 denote the mean potency for all bottles retained for a
period of 1 year. Assume that population variances are unknown but equal. Is the potency for
fresh drugs different from that for stored drugs? Use alpha = .05
Potency Reading for the two samples:
Fresh: 10.2 10.5
10.3
Stored: 9.8
9.6
9.7
Ho = ____________
10.8
9.5
9.8
10.1
10.6
9.6
10.7
10.2
10.2
9.8
10
10.1
10.6
9.9
Ha = ____________
Find the sample mean for fresh bottles____________
( 2 decimal places)
Find the sample mean for stored bottles__________
( 2 decimal places)
Find the sample standard deviation, s1 for fresh bottles_________
( 4 decimal places)
Find the sample standard deviation, s2 for stored bottles________
( 4 decimal places)
Compute the 95% confidence interval for 1 - 2 _____________
Find an estimate of the pooled variance. ______________
(4 decimal places)
Find sp (3 decimals) ____________________ Degrees
of Freedom = ______________
the critical values from the t table at the appropriate degrees of freedom are given by
____________________
The t test statistic is ______________
Estimate the p-value______________
State and interpret your decision: ______________________________________________
In this problem you were asked to perform a pooled variance t-test. Were we justified in
assuming equal variances? To answer this question, conduct a hypothesis test (F test) to check
for equality of variances.
State the null and alternate hypotheses
Ho:
Ha: ________
State the F test statistic _________________________
The numerator and denominator deg of freedom
, ____
State the critical value obtained from the F table ____________
(F table is posted under Lectures on Blackboard for your convenience.)
State your conclusion of this F test. Were we justified in conducting a
pooled variance t test?
_______________________________________________________
_______________________________________________________
_______________________________________________________
______________________________________________(Yes/NO)
TOTAL POINTS FOR #4________
5. (9 points) Consider the paired data shown here:
Pair
1
2
3
4
5
X
21
28
17
24
27
Y
29
30
21
25
33
Difference
In order to test whether the means are equal or not, a t test is performed at alpha = 1%.
a. Ho:
versus
Ha: ____________
b. The mean of the differences = ___________
c. Standard deviation of the differences = _________
(4 decimal places)
d. Degrees of freedom = ____________
e. t test statistic = _____________
f.Critical value(s) for this test = ____________
g. Decision: ____________________________
h. Estimate the P-value_______________
i. Appropriate confidence interval for the difference in means: (________, _______)
TOTAL POINTS FOR #5________
6. (7 points) From a socio-demographic Risk factors in spousal abuse study, it is observed that the
distribution of ages in a sample is as follows:
Age
Number in sample
20-24
103
25-34
216
35-44
171
Total
Conduct a chi-square goodness of fit at the 10 % significance level to test whether the sample
provides a good match to the known age distribution in the population. The known percentages are
18%, 50%, 32%
Ho:
versus
Ha: ____________
The expected number in each category is
_,
, _______
Which group above seems to be underrepresented in the sample?_____________
The chi-squared test statistic is ________________
The critical value from the chi-squared table is _____________
The p-value is ___________
Will you reject Ho? Explain in the context of the problem
_______________________________________________________________
____________________________________________________________________________
TOTAL POINTS FOR #6________
7. (8 points) Sample data has been collected in a study of calcium supplements and their effects on
blood pressure. A placebo group and a calcium group began the study with blood pressure
measurements. The sample values are listed below. At the .05 significance level, test the claim that
the two sample groups come from populations with the same standard deviation.
Placebo: 124.6
104.8
96.5
116.3
106.1
128.8
107.2
123.1
118.1
108.5
120.4
122.5
123.4
102.7
118.1
114.7
120.9
104.4
116.3
109.6
127.7
108
124.3
106.6
121.4
113.2
113.6
Calcium: 129.1
Find the sample standard deviation, for Placebo_________
( 4 decimal places)
Find the sample standard deviation, for Calcium_________
( 4 decimal places)
State the null and alternate hypotheses
Ho:
Ha: ________
Find the test statistic
Find the critical value
State the appropriate degrees of freedom
Draw the appropriate distribution showing the proper critical value. Label all necessary components.
What is your conclusion? Explain
Name
SB ID #:_
_ Your TA
This is worth 5% of your final exam grade. Please print and hand in this original document with your work on
it. Show all work in any blank space provided on each page and enter your final answer on the blank line
provided. You may check your work with a calculator, but all computations must be shown.
1. (14 points) A school administrator wants to compare two reading methods: Method S and
method B. A class of 44 students is randomly divided into two groups of 22 each. One is taught
with method S and the other is taught with B. Is the mean reading score with S higher than with
B? The sample mean reading score for method S was 43.0691, with a standard deviation of
5.5641 and the sample mean reading score for method B was 40.0768 with a standard
deviation of 5.2247. These are sample standard deviations. No alpha is provided for this
problem.
State the null and the alternate hypotheses Ho:
versus Ha: ____________
Assume that the data are independent samples from normal populations with equal population
variances. Thus, we perform a pooled variance t test.
Find an estimate of the pooled variance. ______________
(4 decimal places)
Find sp (3 decimals) ____________________
Degrees of Freedom = ______________
The critical value(s) from the t table at the appropriate degrees of freedom are given by
____________________
The t test statistic is ______________
Estimate the p-value______________
State and interpret your decision:
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
Previously, you were asked to perform a pooled variance t-test.
Were we justified in assuming equal variances? To answer this question please conduct a
hypothesis test (F test) to check for equality of variances.
State the null and alternate hypotheses
Ho: ___________________versus Ha: ______________________
State the F test statistic _________________________
The numerator and denominator degrees of freedom______,_____
State the critical value obtained from the F table ____________
(F table is posted under Lectures on Blackboard for your convenience.)
State your conclusion of this F test. Were we justified in conducting a
pooled variance t test?
_______________________________________________________
___________________________________________________(Yes/NO)
If the pooled variance t test is not warranted, (i.e. if variances are not the same), what test is one
supposed to use to compare the means?
______________________________________________________________
TOTAL POINTS FOR #1________
2. (11 points) David wants to compute whether an alternate route to work would be quicker. For the
next 58 working days he randomly divides his observations into two groups of 29 days each.
He drives the first route for one set of 29 days and drives the second for the other set of 29
days recording, for each day, the commuting times in minutes. Assume that times of
commute are normal.
Route 1
n=29
sample mean = 31.945
s=5.87
Route 2
n=29
sample mean = 28.105
s=6.24
a.
Does the assumption of common population standard deviation seem plausible?
State the null and alternate hypotheses Ho:
b.
versus
Ha:_____________
The numerator and denominator degrees of freedom______,______
c.Give the test statistic_________________
d.
What is your decision regarding common variance
___________________________________________________________________
___________________________________________________________________
e.
State the hypothesis to test if route two is quicker than route one.
Ho:
Ha:_________________________
f. The test statistic is ____
g. The p-value is
h. The degrees of freedom are_______________
i. The decision is __________________________________________________________
Route 2 (does/does not) appear to be quicker.
j. State the F critical value from the F table that was used in part d____________
k.State the pooled variance__________________
TOTAL POINTS FOR #2________
3. (13 points) We would like to compare the characteristics of tuberculosis meningitis in patients
infected with HIV and those who are not infected. In particular, we would like to determine whether
the two populations have the same mean age. A sample of 37 infected patients has mean age 27.9
years and a standard deviation 5.6 years. A sample of 19 patients who are not infected has mean
age 38.8 years and standard deviation 21.7 years. Alpha = .05
Conduct a hypothesis test to check for equality of variances.
State the null and alternate hypotheses
Ho___________________versus Ha:__________
Compute the F test statistic ___________
State the numerator and denominator deg of freedom______,_____
State the critical value obtained from the F table ____________
State your conclusion regarding the variances.
_______________________________________________________
_______________________________________________________
_______________________________________________________
Based on (a), what test will you use to determine if the 2 populations have the same mean
age?
_______________________________________________________
We continue with the test on the next page:
State Ho: ______________________ versus
Ha: ______________________
Find the test statistic __________________
State the degrees of freedom (Welch/Satterthwaite)_____________
State the critical value(s) _____________
State your conclusion, and justify your conclusion using the critical values and the test statistic.
_______________________________________________________
_______________________________________________________
_______________________________________________________
Approximate the P-value for this test. ______________________
State the confidence interval for the difference in means________,________
TOTAL POINTS FOR #3________
4. (18 points) Company officials were concerned about the length of time a particular drug product
retained its potency. A random sample of n1 = 10 bottles of the product was drawn from the
production line and analyzed for potency. A second sample of n2 = 10 bottles was obtained and
stored in a regulated environment for 1 year. Let 1 denote the mean potency for all bottles
coming off the production line and let 2 denote the mean potency for all bottles retained for a
period of 1 year. Assume that population variances are unknown but equal. Is the potency for
fresh drugs different from that for stored drugs? Use alpha = .05
Potency Reading for the two samples:
Fresh: 10.2 10.5
10.3
Stored: 9.8
9.6
9.7
Ho = ____________
10.8
9.5
9.8
10.1
10.6
9.6
10.7
10.2
10.2
9.8
10
10.1
10.6
9.9
Ha = ____________
Find the sample mean for fresh bottles____________
( 2 decimal places)
Find the sample mean for stored bottles__________
( 2 decimal places)
Find the sample standard deviation, s1 for fresh bottles_________
( 4 decimal places)
Find the sample standard deviation, s2 for stored bottles________
( 4 decimal places)
Compute the 95% confidence interval for 1 - 2 _____________
Find an estimate of the pooled variance. ______________
(4 decimal places)
Find sp (3 decimals) ____________________ Degrees
of Freedom = ______________
the critical values from the t table at the appropriate degrees of freedom are given by
____________________
The t test statistic is ______________
Estimate the p-value______________
State and interpret your decision: ______________________________________________
In this problem you were asked to perform a pooled variance t-test. Were we justified in
assuming equal variances? To answer this question, conduct a hypothesis test (F test) to check
for equality of variances.
State the null and alternate hypotheses
Ho:
Ha: ________
State the F test statistic _________________________
The numerator and denominator deg of freedom
, ____
State the critical value obtained from the F table ____________
(F table is posted under Lectures on Blackboard for your convenience.)
State your conclusion of this F test. Were we justified in conducting a
pooled variance t test?
_______________________________________________________
_______________________________________________________
_______________________________________________________
______________________________________________(Yes/NO)
TOTAL POINTS FOR #4________
5. (9 points) Consider the paired data shown here:
Pair
1
2
3
4
5
X
21
28
17
24
27
Y
29
30
21
25
33
Difference
In order to test whether the means are equal or not, a t test is performed at alpha = 1%.
a. Ho:
versus
Ha: ____________
b. The mean of the differences = ___________
c. Standard deviation of the differences = _________
(4 decimal places)
d. Degrees of freedom = ____________
e. t test statistic = _____________
f.Critical value(s) for this test = ____________
g. Decision: ____________________________
h. Estimate the P-value_______________
i. Appropriate confidence interval for the difference in means: (________, _______)
TOTAL POINTS FOR #5________
6. (7 points) From a socio-demographic Risk factors in spousal abuse study, it is observed that the
distribution of ages in a sample is as follows:
Age
Number in sample
20-24
103
25-34
216
35-44
171
Total
Conduct a chi-square goodness of fit at the 10 % significance level to test whether the sample
provides a good match to the known age distribution in the population. The known percentages are
18%, 50%, 32%
Ho:
versus
Ha: ____________
The expected number in each category is
_,
, _______
Which group above seems to be underrepresented in the sample?_____________
The chi-squared test statistic is ________________
The critical value from the chi-squared table is _____________
The p-value is ___________
Will you reject Ho? Explain in the context of the problem
_______________________________________________________________
____________________________________________________________________________
TOTAL POINTS FOR #6________
7. (8 points) Sample data has been collected in a study of calcium supplements and their effects on
blood pressure. A placebo group and a calcium group began the study with blood pressure
measurements. The sample values are listed below. At the .05 significance level, test the claim that
the two sample groups come from populations with the same standard deviation.
Placebo: 124.6
104.8
96.5
116.3
106.1
128.8
107.2
123.1
118.1
108.5
120.4
122.5
123.4
102.7
118.1
114.7
120.9
104.4
116.3
109.6
127.7
108
124.3
106.6
121.4
113.2
113.6
Calcium: 129.1
Find the sample standard deviation, for Placebo_________
( 4 decimal places)
Find the sample standard deviation, for Calcium_________
( 4 decimal places)
State the null and alternate hypotheses
Ho:
Ha: ________
Find the test statistic
Find the critical value
State the appropriate degrees of freedom
Draw the appropriate distribution showing the proper critical value. Label all necessary components.
What is your conclusion? Explain
-
Rating:
/5
Solution: AMS 110 Pretest D Assignment Solution