Math assignment
One. Clark Heter is an industrial engineer at Lyons Products. He would like to determine whether there are more units produced on the night shift than on the day shift. A sample of 50 dayshift workers showed that the mean number of units produced was 353, with a population standard deviation of 25. A sample of 55 nightshift workers showed that the mean number of units produced was 363, with a population standard deviation of 31 units. 
At the .01 significance level, is the number of units produced on the night shift larger? 
(a)  This is a tailed test. 
(b)  The decision rule is to reject if Z < . (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) 
(c)  The test statistic is Z = . (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) 
TWO
Each month the National Association of Purchasing Managers publishes the NAPM index. One of the questions asked on the survey to purchasing agents is: Do you think the economy is contracting? Last month, of the 310 responses, 164 answered yes to the question. This month, 177 of the 291 responses indicated they felt the economy was contracting. 
At the .02 significance level, can we conclude that a larger proportion of the agents believe the economy is contracting this month? 
pc = . (Do not round the intermediate value. Round your answer to 2 decimal places.) 
The test statistic is . (Negative amount should be indicated by a minus sign. Do not round the intermediate value. Round your answer to 2 decimal places.) 
Decision: the null. H0 : π1 ≥ π2
THREE
FOUR

FIVE
When only two treatments are involved, ANOVA and the Student t test (Chapter 11) result in the same conclusions. Also, . As an example, suppose that 14 randomly selected students were divided into two groups, one consisting of 6 students and the other of 8. One group was taught using a combination of lecture and programmed instruction, the other using a combination of lecture and television. At the end of the course, each group was given a 50item test. The following is a list of the number correct for each of the two groups. Using analysis of variance techniques, test the null hypothesis, that the two mean test scores are equal. 
Lecture and Programmed Instruction  Lecture and Television 
12  37 
14  27 
26  37 
28  21 
13  25 
15  27 
26  
23  
(a1)  Complete the ANOVA table. (Round SS, MS and F values to 2 decimal places.) 
Source  SS  df  MS  F 
Factors  
Error  
Total  



(a2)  Use a level of significance. (Round your answer to 2 decimal places.) 
The test statistic is F 
(b)  Using the t test from Chapter 11, compute t. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) 
t 
(c)  There is in the mean test scores 
SIX
The following hypotheses are given. 
Ho : σ1² ≤ σ2² 
H1 : σ1² > σ2² 
A random sample of five observations from the first population resulted in a standard deviation of 12. A random sample of seven observations from the second population showed a standard deviation of 7. At the .01 significance level, is there more variation in the first population? 
The test statistic is . (Round your answer to 2 decimal places.) 
Decision: Ho 
SEVEN
Given the following sample information, test the hypothesis that the treatment means are equal at the .05 significance level. 
Treatment 1  Treatment 2  Treatment 3 
8  3  3 
11  2  4 
10  1  5 
3  4  
2 
(a1)  State the null hypothesis and the alternate hypothesis. 
Null hypothesis 
Ho: μ1 = μ2 = μ3  
Ho: μ1 = μ2 
a2)  Alternative hypothesis 
H1: Treatment means are all the same  
H1: Treatment means are not all the same 
b)  What is the decision rule? (Round your answer to 2 decimal places.) 
Reject Ho if F > 
c)  Compute SST, SSE, and SS total. (Round your answers to 2 decimal places.) 
SST  
SSE  
SS total  


d)  Complete an ANOVA table. (Round F, SS to 2 decimal places and MS to 3 decimal places.) 
Source  SS  df  MS  F 
Treatments  
Error  
Total 
e)  State your decision regarding the null hypothesis. 
Reject H0.  
Do not reject H0. 
f)  If H0 is rejected, can we conclude that treatment 1 and treatment 2 differ? Use the 95 percent level of confidence. 
, we conclude that the treatments 1 and 2 have different means. 
EIGHT
There are four radio stations in Midland. The stations have different formats (hard rock, classical, country/western, and easy listening), but each is concerned with the number of minutes of music played per hour. From a sample of 10 hours from each station, the following sample means were offered. 
SS total = 650.75 
(a)  SST = . (Round your answer to 3 decimal places.) 
(b)  SSE = . (Round your answer to 3 decimal places.) 
(c)  Complete an ANOVA table. (Round SS, MS, F to 3 decimal places and df to nearest whole number.) 
SS  df  MS  F  
Treatments  
Error  
Total  



(d)  At the .05 significance level, is there a difference in the treatment means? 
NINE
Given the following sample information, test the hypothesis that the treatment means are equal at the .05 significance level. 
Treatment 1  Treatment 2  Treatment 3 
3  9  6 
2  6  3 
5  5  5 
1  6  5 
3  8  5 
1  5  4 
4  1  
7  5  
6  
4  
Click here for the Excel Data File 
(a)  Ho : μ1 μ2 μ3. 
H1 : Treatment means all the same 
(b)  Reject Ho if F > .(Round your answer to 2 decimal places.) 
(c)  SST = SSE = SS total = (Round your answers to 2 decimal places.) 
(d)  Complete the ANOVA table. (Round SS, MS and F values to 2 decimal places.) 
Source  SS  df  MS  F 
Treatments  
Error  
Total  



(e)  Decision: Ho 
(f)  Find the 95% confidence interval for the difference between treatment 2 and 3. (Round your answers to 2 decimal places.) 
95% confidence interval is: ±  
We can conclude that the treatments 2 and 3 are 
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