Listed below are ages of actresses and actors at the time th

Listed below are ages of actresses and actors at the time that they won an award for the categories of Best Actress and Best Actor. Use the sample data to test for a difference between the ages of actresses and actors when they win the award. Use a 0.05 significance level. Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal Actress\'s age 20 35 21 Actor\'s age 53 44 49 60 51 30 42 In this example, d is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the actress\'s age minus the actor\'s age. What are the null and alternative hypotheses for the hypothesis test? Identify the test statisti t=| | (Round to two decimal places as needed.)

Solution

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

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At level of significance =    0.05      
As you can see, this is a    2   tailed test.  
          
Calculating the standard deviation of the differences (third column):          
          
s =    13.67926249      
          
Thus, the standard error of the difference is sD = s/sqrt(n):          
          
sD =    4.325762617      
          
Calculating the mean of the differences (third column):          
          
XD =    -8.7      
          
As t = [XD - uD]/sD, where uD = the hypothesized difference =    0   , then  
          
t =    -2.011206062   [ANSWER, ITEM 2]

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As df = n - 1 =    4      
                      
Using p values,
          
p =    0.114641153   [ANSWER, ITEM 3]