Data for the ages of grooms and their brides for a random sa

Data for the ages of grooms and their brides for a random sample of 31 couples in a certain county are provided. Complete parts a through c below. Click the icon to view the data. Find and compare the sample means. The sample mean for the grooms, is (Round to three decimal places as needed.) Test the hypothesis that there is a significant difference in mean ages of brides and grooms, using a significance level of 0.05. Determine the hypotheses for this test. Let mu difference be the population mean difference between the ages of grooms and their brides, in years. Choose the correct answer below. than the sample mean for their brides, Choose the correct answer below. Find the test statistic for this test.

Solution

a)

Xgroom = 27.77419355
Xbride = 25.5483871

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Let ud = u2 - u1.              
Formulating the null and alternative hypotheses,              
              
Ho:   ud   =   0  
Ha:   ud   =/=   0 [OPTION E]

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At level of significance =    0.05          
As we can see, this is a    two   tailed test.      
              
Calculating the standard deviation of the differences (third column):              
              
s =    2.642091058          
              
Thus, the standard error of the difference is sD = s/sqrt(n):              
              
sD =    0.474533563          
              
Calculating the mean of the differences (third column):              
              
XD =    2.225806452          
              
As t = [XD - uD]/sD, where uD = the hypothesized difference =    0   , then      
              
t =    4.69051428 = 4.69   [ANSWER, TEST STATISTIC]

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Extra info:

As df = n - 1 =    30          
              
Then the critical value of t is              
              
tcrit =    +/-   2.042272456      
              
Thus, comparing t and tcrit, we   WE REJECT THE NULL HYPOTHESIS.          
              
Also, using p values,              
              
p =        5.57511E-05      
              
Also, comparing this p to the significance level,   WE REJECT THE NULL HYPOTHESIS.