The following is sample information. Test the hypothesis that the treatment means are equal. Use the 0.05 significance level.
Treatment 1
Treatment 2
Treatment 3
5
5
6
5
4
6
8
6
6
9
3
5
(b)
What is the decision rule? (Round your answer to 2 decimal places.)
Reject H_{0} if the test statistic is greater than .
(c&d)
Compute SST, SSE, and SS total and complete an ANOVA table. (Round SS, MS and F values to 3 decimal places.)
Source
SS
df
MS
F
Treatments
Error
Total
The following is sample information. Test the hypothesis that the treatment means are equal. Use the 0.05 significance level. 
Treatment 1  Treatment 2  Treatment 3 
5  5  6 
5  4  6 
8  6  6 
9  3  5 
(b)  What is the decision rule? (Round your answer to 2 decimal places.) 
Reject H_{0} if the test statistic is greater than . 
(c&d)  Compute SST, SSE, and SS total and complete an ANOVA table. (Round SS, MS and F values to 3 decimal places.) 
Source  SS  df  MS  F 
Treatments 




Error 


 
Total 

 
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A sample of 42 observations is selected from one population with a population standard deviation of 3.1. The sample mean is 101.0. A sample of 52 observations is selected from a second population with a population standard deviation of 4.0. The sample mean is 99.8. Conduct the following test of hypothesis using the 0.04 significance level. 
H_{0} : ?_{1} = ?_{2} 
H_{1} : ?_{1} ? ?_{2} 
(b)  State the decision rule. (Negative amounts should be indicated by a minus sign. Round your answer to 2 decimal places.) 
The decision rule is to reject H_{0} if z is outside the interval (, ). 
(c)  Compute the value of the test statistic. (Round your answer to 2 decimal places.) 
Value of the test statistic 
(e)  What is the pvalue? (Round your answer to 4 decimal places.) 
pvalue 
*** Please see p. 2 for Question 2 ***
Question 2 (7 points)
The following Excel output shows the outcome of a linear regression of individuals%u2019 wage per hour (in dollars) on the number of years they attended school (in years).
SUMMARY OUTPUT  
Regression Statistics  
Multiple R  0.381932619  
R Square  0.145872525  
Adjusted R Square  0.144267022  
Standard Error  4.753758428  
Observations  534  
ANOVA  
df  SS  MS  F  Significance F  
Regression  1  2053.22554  2053.22554  90.8578469  5.45998E20  
Residual  532  12022.25261  22.59821919  
Total  533  14075.47815  
Coefficients  Standard Error  t Stat  Pvalue  Lower 95%  Upper 95%  Upper 95.0%  
Intercept  0.745942699  1.045403804  0.71354504  0.475821452  2.799566599  1.307681201  1.307681201  
Years of School  0.750448943  0.078729942  9.531938255  0.000545998  0.595789385  0.9051085  0.9051085 
Part (a) (1 point)
What is the value of the estimated slope %u201Cb%u201D?
Part (b) (2 points)
Interpret the estimated value of the slope (i.e., explain what the number means in this regression).
Part (c) (1 point)
Is the estimate of the slope statistically significant? Please answer %u201Cyes%u201D or %u201Cno%u201D and explain how you can tell.
Part (d) (2 points)
Explain why we want to be able to reject the null hypothesis H0: %u03B2 = 0.
Part (e) (1 point)
How much of the total variation in wages can be explained by individuals%u2019 education?
1  Which of the following statements about Type I and Type II errors is correct  
a  Type I: Reject a true alternative hypothesis. Type II: Do not reject a false alternative.  
b  Type I: Reject a true null hypothesis. Type II: Do not reject a false null hypothesis.  
c  Type I: Reject a false null hypothesis. Type II: Reject a true null hypothesis.  
d  Type I: Do not reject a false null hypothesis. Type II: Reject a true null hypothesis.  
2  You are reading a report that contains a hypothesis test you are interested in. The writer of the report writes that the pvalue for the test you are interested in is 0.0749, but does not tell you the value of the test statistic. From this information you can:  
a  Not reject the hypothesis at a Probability of Type I error = .05, but reject the hypothesis at a Probability of Type I error = 0.10  
b  Reject the hypothesis at a Probability of Type I error = .05, and reject at a Probability of Type I error = 0.10  
c  Not reject the hypothesis at a Probability of Type I error = 0.05, and not reject at a Probability of Type I error = 0.10  
d  Reject the hypothesis at a Probability of Type I error = .05, but not reject at a Probability of Type I error = 0.10  
3  The random sample below is obtained to test the following hypothesis about the population mean.  
H?: ? ?  1500  
H?: ? >  1500  
620  1711  366  2528  2678  1661  442  725  1938  
409  330  2480  542  369  2124  549  2074  1665  
1873  873  2143  2061  1177  2509  1264  2397  1523  
1837  1958  1041  1639  2199  2232  387  2270  2136  
1111  1883  2612  2230  1597  1726  694  1990  1354  
2090  909  2128  1608  747  1121  2220  2390  2347  
1041  316  655  632  2064  1901  532  552  846  
2704  1410  2165  1065  937  1452  2539  410  656  
1169  527  809  2364  2350  2210  1459  2391  856  
2711  1985  2382  2289  1927  518  2177  437  1151  
2018  1580  607  2715  2188  1691  1394  2610  1186  
695  2428  2246  858  2036  1681  2449  1578  1971  
1846  1729  2389  1737  1913  1863  2072  2593  2287  
2220  2230  551  458  2626  2731  488  2551  1736  
1373  307  1803  2647  2679  1508  1468  1443  516  
1002  2116  2616  817  2522  460  1879  1999  1837  
The level of significance of the test is ? = 0.05. Compute the relevant test statistic.  
This is a(n) _______ (twotail, uppertail, lowertail) test. The test statistic is TS = _______.  
a  Twotail test  TS =  1.81  
Do not reject H?: ? ? 1500. Conclude that the population mean is not greater than 1500.  
b  Upper tail test.  TS =  1.52  
Do not reject H?: ? ? 1500. Conclude that the population mean is not greater than 1500.  
c  Upper tail test.  TS =  1.81  
Reject H?: ? ? 1500. Conclude that the population mean is greater than 1500.  
d  Lower tail test.  TS =  1.98  
Do not reject H?: ? ? 1500. Conclude that the population mean is no greater than 1500.  
4  Consider the following hypothesis test.  
H?: ? ?  30  
H?: ? >  30  
A random sample of n = 15 yielded the following observations  
51  38  26  16  28  
57  20  33  35  23  
21  47  56  54  36  
Use ? =  0.05  
TS = ______  CV = ______  State the decision rule.  
a  1.68  1.761  Do not reject H?. Conclude the mean is not greater than 30.  
b  1.68  1.64  Reject H?. Conclude the mean is greater than 30.  
c  1.847  2.145  Do not reject H?. Conclude the mean is not less than 30.  
d  1.847  1.761  Reject H?. Conclude the mean is less than 30.  
5  In a recent study, a major fast food restaurant had a mean service time of 165 seconds. The company embarks on a quality improvement effort to reduce the service time and has developed improvements to the service process. The new process will be tested in a sample of stores. The new process will be adopted in all of its stores, if it reduced mean service time by more than 45 seconds compared to the current mean service time. To perform the hypothesis test, the sample of 48 stores yields the following data (seconds).  
90  96  133  108  136  110  119  138  
129  98  101  92  135  124  115  90  
132  125  110  124  126  138  94  130  
108  96  140  135  102  114  109  137  
138  104  108  134  92  107  96  119  
105  111  96  136  126  116  98  131  
Use ? =  0.05  
TS = ______  CV = ______  
a  1.548  1.678  Do not reject H?. The mean service time is not reduced by more than 45 seconds. Do not adopt the new process.  
b  1.871  1.678  Reject H?. The mean service time is reduced by more than 45 seconds. Adopt the new process.  
c  1.871  1.640  Do not reject H?. The mean service time is not reduced by more than 45 seconds. Do not adopt the new process.  
d  1.548  1.640  Reject H?. The mean service time is reduced by more than 45 seconds. Adopt the new process.  