Question

7. You are studying a cholera outbreak in one part of Mali. Some villages have been hit harder by the outbreak than others. Moreover, some villages have more homes with indoor flush toilets, which reduce people’s exposure to human waste that can spread cholera. With data from just four villages, can you show the relationship between cholera rates and flush toilets to be statistically significant?

village : 1, 2, 3, 4

percentage of homes with flush toilets : 15, 20, 5, 80

cases of cholera per 1000 residents: 9, 4, 12, 2

A. State appropriate null and alternative hypotheses. (6 points)

B. Caldwell’s table of critical values doesn’t go down to 2 df, so I’ll give it to you. The critical value at the .05 level of significance is |0.95|. But you tell me: is it positive or negative here? (4 points)

C. Make a scatterplot for these data. Pay attention to which variable is X and which is Y. (5 points)

D. Calculate the test statistic. Pay attention to which variable is X and which is Y. Keep things tidy and label steps clearly so that your grader can figure out what you’re doing. (10 points)

E. Give a proper English statement of your conclusion and what your conclusion means in terms of error(s) risked and hypotheses rejected or not. Make reference to the particulars of this problem (flush toilets, cholera rates). (10 points)

F. Calculate and interpret the coefficient of determination. (5 points)

Answer 1

Solution :

Here, X denotes the percentage of home with flush toilets

an Y denotes the cases of chlorea per 1000 residents.

1. We want to whether there is significant relationship between X and Y. Let denotes the correlation between X and Y.

a)

The null and alternative hypotheses will be

vs

This corresponds to two tailed test.

b)

Based on the information present, the significance level =0.05 and the critical value for two tailed test is

The rejection region for two tailed test is  

Critical will be both considered as positive and negative.

c)

Considering the scatter plot we will considered as Y= cases of chlorea per 1000 residents. and X= percentage of home with flush toilets. As chlorea is dependent variable and it is effected bt the hygeine.

d)

The test statistic will be

Since it is observed that , it is concluded that the null hypothesis is not rejected.

Using p-value approach, the p-value is 0.194 > 0.05, hence null hypothesis is not rejected.

e)

Hence, there is no significant relationship between percentage of home with flush toilets and the cases of chlorea per 1000 residents.

f)

The pearson correlation coefficient is calculated as

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