Question 2: One of the UNEP study looked at access to potable water in the Carib

Question

Question 2:

One of the UNEP study looked at access to potable water in the Caribbean. A random sample of 600 rural residents was taken and it was found that 74.5% of them had access to potable water. A random sample of 600 urban residents was taken and it was found that 72% of them had access to potable water. UNEP representatives want to know if there is sufficient evidence that a higher percentage of rural residents have access to potable water than urban residents in the Caribbean.

a. Set up appropriate hypotheses based on the question of interest.

b. If the percentages of rural and urban residents with access to potable water were equal, what would your best estimate of that percentage be?

c. Complete the assumptions and mechanics steps of your hypothesis test, showing your work.

Assumptions (check):

Test statistic

p-value computations:

Interpretation of p-value (not reporting the result, but what is the meaning of this number)

State your conclusion in context of the problem using =0.05 significance level.

d. Now, use the critical value approach to answer the same question.

e. Calculate an appropriate confidence interval (two sided or one sided) and explain how it can be used to do this test

Explanation / Answer

p1 = 0.745

p2 = 0.72

H0: p1 = p2

H1: p1 > p2

The Pooled sample proportion P = (p1 * n1 + p2 * n2)/(n1 + n2) = (0.745 * 600 + 0.72 * 600)/1200 = 0.7325

SE = sqrt (P * (1 - P) * (1/n1 + 1/n2))

= sqrt (0.7325 * 0.2675 * (1/600 + 1/600))

= 0.0256

The test statistic Z = (p1 - p2)/SE

= (0.745 - 0.72)/0.0256 = 0.98

P - value = P(Z > 0.98)

= 1 - P(Z < 0.98)

= 1 - 0.8365

= 0.1635

As the p-value is greater than the significance level (0.1635 > 0.05), so the null hypothesis is not rejected.

So there is not sufficient evidence that a higher percentage of rural residents have access the potable water than urban residents in Caribbean.

At 0.05, significance level the critical value is 1.96

As the critical value is greater than the test statistic value (1.96 > 0.98), so the null hypothesis is not rejected.

The confidence interval is

(p1 - p2) +/- z* * SE

= (0.745 - 0.72) +/- 1.96 * 0.0256

= 0.025 +/- 0.05

= -0.025, 0.075

As the th confidence interval contains the hypothized value 0, so the null hypothesis is not rejected.

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