Question

Researchers interviewed street prostitutes in Canada and the United States. The mean age of the 100 Canadian prostitutes upon entering prostitution was 20 with a standard deviation of seven. The mean age of the 130 United States prostitutes upon entering prostitution was 22 with a standard deviation of eight. Is the mean age of entering prostitution in Canada lower than the mean age in the United States? Test at a 1% significance level. NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

1.)What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.)

2.)What is the p-value? (Round your answer to four decimal places.)

3.)Explain what the p-value means for this problem.

a- If H0 is false, then there is a chance equal to the p-value that the sample mean age of entering prostitution in Canada is at least 2 more than the sample mean age of entering prostitution in the United States.

b- If H0 is true, then there is a chance equal to the p-value that the sample mean age of entering prostitution in Canada is at least 2 more than the sample mean age of entering prostitution in the United States.

c- If H0 is true, then there is a chance equal to the p-value that the sample mean age of entering prostitution in Canada is at least 2 less than the sample mean age of entering prostitution in the United States.

d- If H0 is false, then there is a chance equal to the p-value that the sample mean age of entering prostitution in Canada is at least 2 less than the sample mean age of entering prostitution in the United States.

4.) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value.

5.) Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion.

(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)

(iii) Reason for decision:

a- Since p-value > α, we reject the null hypothesis.

b- Since p-value > α, we do not reject the null hypothesis.

c-Since p-value < α, we do not reject the null hypothesis.

d-Since p-value < α, we reject the null hypothesis.

Answer 1

Ho :   µ1 - µ2 =   0                  
Ha :   µ1-µ2 <   0                  
                          
Level of Significance ,    α =    0.01                  
                          
Sample #1   ---->   sample 1                  
mean of sample 1,    x̅1=   20.00                  
standard deviation of sample 1,   s1 =    7.00                  
size of sample 1,    n1=   100                  
                          
Sample #2   ---->   sample 2                  
mean of sample 2,    x̅2=   22.00                  
standard deviation of sample 2,   s2 =    8.00                  
size of sample 2,    n2=   130                  
                          
difference in sample means =    x̅1-x̅2 =    20.0000   -   22.0   =   -2.00  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    7.5820                  
std error , SE =    Sp*√(1/n1+1/n2) =    1.0085                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   -2.0000   -   0   ) /    1.01   =   -1.983
                          
Degree of freedom, DF=   n1+n2-2 =    228                  

p-value =        0.0243   [ excel function: =T.DIST(t stat,df) ]               

Conclusion:

p-value>α , Do not reject null hypothesis

   

THANKS

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