Question

Exercise 1

The table below shows results from the New Mexico Behavioral Risk Factor Surveil-

lance System (BRFSS), an annual survey conducted by telephone. Data are shown

for the years 2011 and 2015. Each year represents a different random sample. The

results below indicate the sample size and number of people who reported that they

have been diagnosed with diabetes.

Diagnosed with diabetes

Year	yes	no	total
2011	1189	8135	9324
2015	908	5617	6525

Conduct a hypothesis test of whether there was a difference in the proportion of New

Mexicans with diabetes between 2011 and 2015. When conducting the hypothesis

test, be sure to

1. State the null and alternative hypotheses

2. Calculate the test statistic

3. Report the p-value for the test statistic

4. State your conclusion in words

Answer 1

we have p1 = (1189/9324) = 0.13

and p2 = (908/6525) = 0.14

n1 =9324 and n2 = 6525

(1) Null hypothesis:- there is no significant difference between the two proportions

Alternate hypothesis:- there is significant difference between the two proportions

(2)we have the following formula test statistic

z=

setting the given values, we get

z=

this gives us z=

(3) Using standard normal distribution, the p value corresponding to the z score of -1.81 is

p value= 0.0703

(4) since the p value is greater than 0.05 significance level, so we can say that the p value is significant and we fail to reject the null hypothesis

thus, we can say that we have insufficient evidence to support the claim that there is significant difference between the means.