Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations. Use the t-table. H 0 : µ 1 - µ 2 = 0 H A : µ 1 - µ 2 = 249 = 272 s 1...

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Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations. Use the t-table.

H
0:
µ
1
-
µ
2
= 0

HA
:
µ
1
-
µ
2

















= 249		= 272

s
1
= 35
s
2
= 23

n
1
= 10
n
2
= 10









a-1.
Calculate the value of the test statistic under the assumption that the population variances are unknown but equal.
(Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)







Test statistic









a-2.
Calculate the critical value at the 5% level of significance.
(Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)







Critical value











b-1.
Calculate the value of the test statistic under the assumption that the population variances are unknown and are not equal.
(Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)







Test statistic









b-2.
Calculate the critical value at the 5% level of significance.
(Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)







Critical value


No 3
1.11 points







Consider the following sample data drawn independently from normally distributed populations with equal population variances. Use the t value.











































Sample 1Sample 2
12.1
8.9
9.5
10.9
7.3
11.2
10.2
10.6
8.9
9.8
9.8
9.8
7.2
11.2
10.2
12.1








Click here for the Excel Data File














a.
Construct the relevant hypotheses to test if the mean of the second population is greater than the mean of the first population.














H
0:
µ
1
-
µ
2
= 0;
HA
:
µ
1
-
µ
2

H
0:
µ
1
-
µ
2
= 0;
HA
:
µ
1
-
µ
2
> 0

H
0:
µ
1
-
µ
2
= 0;
HA
:
µ
1
-
µ
2
? 0










b-1.
Calculate the value of the test statistic.
(Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)







Test statistic









b-2.
Calculate the critical value at the 1% level of significance.
(Negative value should be indicated by a minus sign.
Round your answer to 3 decimal places.)







Critical value














b-3.
Interpret the results.










Do not reject
H
0
Reject
H
0










c-1.
Calculate the critical value at the 10% level of significance.
(Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)







Critical value


No 4
1.11 points







David Anderson has been working as a lecturer at Michigan State University for the last three years. He teaches two large sections of introductory accounting every semester. While he uses the same lecture notes in both sections, his students in the first section outperform those in the second section. He believes that students in the first section not only tend to get higher scores, they also tend to have lower variability in scores. David decides to carry out a formal test to validate his hunch regarding the difference in average scores. In a random sample of 18 students in the first section, he computes a mean and a standard deviation of 77.4 and 10.8, respectively. In the second section, a random sample of 14 students results in a mean of 74.1 and a standard deviation of 12.2.











a.
Construct the null and the alternative hypotheses to test David’s hunch.











b-1.
Calculate the value of the test statistic.
(Round your answer to 2 decimal places.)







Test statistic


No 6.
1.11 points







An engineer wants to determine the effectiveness of a safety program. He collects annual loss of hours due to accidents in 12 plants “before and after” the program was put into operation. The data can be found on the text website, labeled

Safety Program
. Use the t table.




























































PlantBeforeAfterPlantBeforeAfter
1100
98
7
88
90
290
88
8
75
70
394
90
9
65
62
485
86
10
58
60
570
67
11
67
60
683
80
12
104
98











a.
Specify the competing hypotheses that determine whether the safety program was effective.









b.
Assuming that hours are normally distributed, calculate the value of the test statistic.
(Round your answer to 2 decimal places.)







Test statistic











c.
At the 5% significance level, calculate the critical value.
(Round your answer to 3 decimal places.)







Critical value














d.
Is there sufficient evident to conclude that the safety program was effective?










No
Yes

005_m8nuazo-dlqv44md.docx
Answered Same DayDec 22, 2021

Answer To: Consider the following competing hypotheses and accompanying sample data drawn independently from...

David answered on Dec 22 2021
117 Votes
No.  2.
value:
1.11 points
 
    Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations. Use the t-table.
     
    H0: μ1 − μ2 ≥ 0
    HA: μ1 − μ2 < 0
       = 249
    = 272
      s1 = 35
    s2 = 23
      n1 = 10
    n2 = 10
    a-1.
    Calculate the value of the test statistic under the assumption that the population variances are unknown but equal. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)
      Test statistic
    
-1.74
 
    a-2.
    Calculate the critical value at the 5% level of significance. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)
      Critical value
    
-1.734
 
    b-1.
    Calculate the value of the test statistic under the assumption that the population variances are unknown and are not equal. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)
      Test statistic
    
-1.74
 
    b-2.
    Calculate the critical value at the 5% level of significance. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)
      Critical value
    
-1.753
 
    Pooled-Variance t Test for the Difference Between Two Means
    (assumes equal population variances)
    
    Data
    Hypothesized Difference
    0
    Level of Significance
    0.05
    Population 1 Sample
     
    Sample Size
    10
    Sample Mean
    249
    Sample Standard Deviation
    35
    Population 2 Sample
     
    Sample Size
    10
    Sample Mean
    272
    Sample Standard Deviation
    23
    
    
    Intermediate Calculations
    Population 1 Sample Degrees of Freedom
    9
    Population 2 Sample Degrees of Freedom
    9
    Total Degrees of Freedom
    18
    Pooled Variance
    877
    Standard Error
    13.2439
    Difference in Sample Means
    -23
    t Test Statistic
    -1.7367
    
    
    Lower-Tail Test
     
    Lower Critical Value
    -1.7341
    p-Value
    0.0498
    Reject the null hypothesis
     
    Separate-Variances t Test for the Difference Between Two Means
    (assumes unequal population variances)
    Data
    Hypothesized Difference
    0
    Level of Significance
    0.05
    Population 1 Sample
     
    Sample Size
    10
    Sample Mean
    249
    Sample Standard Deviation
    35.0000
    Population 2 Sample
     
    Sample Size
    10
    Sample Mean
    272
    Sample Standard Deviation
    23.0000
    
    
    Intermediate Calculations
    Numerator of Degrees of Freedom
    30765.1600
    Denominator of Degrees of Freedom
    1978.2956
    Total Degrees of Freedom
    15.5513
    Degrees of Freedom
    15
    Standard Error
    13.2439
    Difference in Sample Means
    -23
    Separate-Variance t Test Statistic
    -1.7367
    
    
    Lower-Tail Test
     
    Lower Critical Value
    -1.7531
    p-Value
    0.0515
    Do not reject the null hypothesis
     
    
    
No 3
1.11 points
 
    Consider the following sample data drawn independently from normally distributed populations with equal population variances. Use the t value.
    Sample 1
    Sample 2
    12.1
    8.9
    9.5
    10.9
    7.3
    11.2
    10.2
    10.6
    8.9
    9.8
    9.8
    9.8
    7.2
    11.2
    10.2
    12.1
    
    
Click here for the Excel Data File
    a.
    Construct the relevant hypotheses to test if the mean of the second population is greater than the mean of the first population.
     
     
H0: μ1 − μ2 = 0; HA: μ1 − μ2 ≠
    
    
    b-1.
    Calculate the value of the test statistic. (Negative value...
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