Question

A philanthropic organization helped a town in Africa dig several wells to gain access to clean water. Before the wells were in place, an average of 120 infants contracted typhoid each month. After the wells were installed, the philanthropic organization surveyed for nine months and found an average of 90 infants contracted typhoid per month. Assume that the population standard deviation is 40 and the number of infants that contract typhoid is normally distributed. Specify the null and alternative hypotheses to determine whether the average number of infants that contract typhoid has decreased because the wells were put in place.

Answer 1

H0 : μ = 120

H1 : μ < 120

We Can conclude that the number of infants that contract typhoid has reduced because the wells were put in place.

Explanation:

Average Number of infants who contracted typhoid monthly = 120

Average Number of infants who contracted typhoid monthly after well installation = 90

The null and alternative hypothesis :

H0 : μ = 120

H1 : μ < 120

Obtain the test statistic :

(Xbar - μ) ÷ s/sqrt(n)

(90 - 120) ÷ 40/sqrt(9)

-30 ÷ 13.3333

= - 2.25

The Pvalue at 95% confidence, df = n-1 = 9 - 1 = 8

Tcritical at 95%, df = 8 ; one tailed = 0.02728

Decision region :

Pvalue < α ; Reject H0

0.02728 < 0.05 ; Hence, we conclude that there is significant evidence that the average number of infants that contract typhoid has decreased because the wells were put in place.