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 nine. 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 is:

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

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

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

Using the data of t-value and degree of freedom;  

The P-value = -0.224

Decision rule: Do not 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 ∝.

Therefore, there is enough evidence to conclude that the mean age of entering prostitution in Canada is lower than that of the United States.