Question

Researchers interviewed street prostitutes in Canada and the United States. The mean age of the 100 Canadian prostitutes upon entering prostitution was 18 with a standard deviation of seven. The mean age of the 130 United States prostitutes upon entering prostitution was 20 with a standard deviation of nine. 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.)

Part (d)
State the distribution to use for the test. (Enter your answer in the form z or tdf where df is the degrees of freedom. Round your answer to two decimal places.)
  

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


(f part 2)Explain what the p-value means for this problem.

• 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.

• 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.    

• 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.

• 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.

Answer 1

Result:

Researchers interviewed street prostitutes in Canada and the United States. The mean age of the 100 Canadian prostitutes upon entering prostitution was 18 with a standard deviation of seven. The mean age of the 130 United States prostitutes upon entering prostitution was 20 with a standard deviation of nine. 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.)

Part (d)
State the distribution to use for the test. (Enter your answer in the form z or tdf where df is the degrees of freedom. Round your answer to two decimal places.)
  

t distribution used.

df= 100+130-2=228

Part (e)
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.)
test statistic = -1.836

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

P value = 0.0339

(f part 2)Explain what the p-value means for this problem.

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.

calculations:

Ho: µ1 = µ2   H1: µ1 < µ2

Lower tail test

Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference	0
Level of Significance	0.01
Population 1 Sample
Sample Size	100
Sample Mean	18
Sample Standard Deviation	7
Population 2 Sample
Sample Size	130
Sample Mean	20
Sample Standard Deviation	9
Intermediate Calculations
Population 1 Sample Degrees of Freedom	99
Population 2 Sample Degrees of Freedom	129
Total Degrees of Freedom	228
Pooled Variance	67.1053
Standard Error	1.0896
Difference in Sample Means	-2.0000
t Test Statistic	-1.8355
Lower-Tail Test
Lower Critical Value	-2.3428
p-Value	0.0339
Do not reject the null hypothesis