Question

90. 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 six. The mean age of the 130 United States prostitutes upon entering prostitution was 20 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.

Short answer

There is lack of evidence from the sample data to declare that the mean age of entry into prostitution in Canada is lower than the mean age in the United States at the $1\%$ level of significance.

Step-by-step solution

Given information

Let, the mean age of the $100$Canadian prostitutes upon entering prostitution was $18$with a standard deviation of six. And the mean age of the $130$United States prostitutes upon entering prostitution was $20$ with a standard deviation of eight.

Explanation

Let, 2 means, independent sample, and the population standard deviations unknown.
Then the random variable is $\overline{X_1}-\overline{X_2}$
The hypothesis are:
$H_0:{\mu }_1={\mu }_2$
$H_0:{\mu }_1<{\mu }_2$
In Canada, the average age of entry into prostitution is lower than in the United States.

The $p-$value for graph lift tailed:$0.0157$
Decision: do no reject $H_0$.
As a result, there is lack of evidence from the sample data to declare that the mean age of entry into prostitution in Canada is lower than the mean age in the United States at the $1\%$ level of significance.