Question

For the following test, assume that the two samples are independent simple random samples selected from normally distributed populations and that the population standard deviations are equal (1 = 02) so that the standard error of the difference between means is obtained by pooling the sample variances. A researcher was interested in comparing the amount of time spent studying baboons by women and men from a group of anthropologists. Independent simple random samples of 32 women and 30 men were selected, and each person was asked how many hours they had studied the baboons during the previous week. The summary is shown in the table. Women ny - 32 women = 19.5 hours 51 - 1.3 hours Men m2 - 30 men 22 - 18.1 hours 52 - 2.2 hours Use a 0.05 significance level to test the claim that the mean amount of time spent studying baboons by women is smaller than it is for men. What are the correct hypotheses? (Select the correct symbols and use decimal values not percentages.) Ho: Select an answer Select an answer Hy: Select an answer Select an answer Original Claim - Select an answer Based on the hypotheses, find the following: Test Statistic (Round to three decimal places.) p.value (Round to four decimal places.) Critical value(s) - (Round to three decimal places.)

Answer 1

Ho :   µ1 - µ2 =   0                  
Ha :   µ1-µ2 <   0                  
                          

claim : µ1 < µ2

Level of Significance ,    α =    0.05                  
                          
Sample #1   ---->  female
mean of sample 1,    x̅1=   19.50                  
standard deviation of sample 1,   s1 =    1.30                  
size of sample 1,    n1=   32                  
                          
Sample #2   ---->   male
mean of sample 2,    x̅2=   18.10                  
standard deviation of sample 2,   s2 =    2.20                  
size of sample 2,    n2=   30                  
                          
difference in sample means =    x̅1-x̅2 =    19.5000   -   18.1   =   1.40  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    1.7923                  
std error , SE =    Sp*√(1/n1+1/n2) =    0.4555              

Degree of freedom, DF=   n1+n2-2 =    60    
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   1.4000   -   0   ) /    0.46   =   3.074
                          
               
p-value =        0.9984

t-critical value , t* =        -1.671      

Decision:   | t-stat | > | critical value |, so, Reject Ho      

conclusion : there is not sufficient evidence that mean time for women is smaller than men

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THANKS

revert back for doubt

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