Question

Researchers interviewed street prostitutes in Canada and the United States. The mean age of the 100 Canadian prostitutes upon entering prostitution was 19 with a standard deviation of seven. The mean age of the 130 United States prostitutes upon entering prostitution was 21 with a standard deviation of eight. Is the mean age of entering prostitution in Canada lower than the mean age in the United States

Answer 1

Answer:

Step-by-step explanation:

The null and the alternative hypothesis can be computed as:

$H_o: \mu_{c} \ge \mu_{us}$

$H_a: \mu_{c} < \mu_{us}$

The t- student test statistics can be computed as:

$t = \dfrac{ x_c - x_{us} }{\sqrt { \dfrac{\sigma_c^2}{n_c} + \dfrac{\sigma_{us} ^2}{n_{us}} } }$

$t = \dfrac{ 19 - 21 }{\sqrt { \dfrac{7^2}{100} + \dfrac{8^2}{130} } }$

t = -2.017

degree of freedom = (n₁-1)+(n₂-1)

= (100-1) + (130-1)

= 228

At t = -2.017 and 228 df

P-value = -0.224

Decision rule: Not to reject the null hypothesis if the p-value is greater than ∝(0.01)

Conclusion: We reject the null hypothesis since the p-value is less than ∝.

Thus, there is sufficient evidence to conclude that the mean age of entering prostitution in Canada is lower than that of the United states.