Verizon LTE 64% 12:57 PM ecat.montana.edu 1. Recall from Exam 2: The city counci

Question

Verizon LTE 64% 12:57 PM ecat.montana.edu 1. Recall from Exam 2: The city council of Bozeman is interested in estimating the proportion of its citizens that are overweight or obese and comparing this rate to the national average of 69%. The city council randomly samples 150 adults 20 years of age or older and 87 reported that they are overweight or obese. Is there evidence to suggest that Bozeman residents are healthier than the US as a whole? a. Identify and define the parameter of interest in context of the problem. b. Set-up the hypotheses of interest to the city council using both statistical notation and words. explaining what they mean in c. Calculate the test statistic associated with the hypotheses in part b. d. Using R, calculate the p-value for this hypothesis test. Provide an interpretation of the p- value in context of the problem. e. Provide an appropriate conclusion at the 5% significance level.

Explanation / Answer

a) Parameter of interest is proportion, p

b)
Below are the null and alternate hypothesis
H0: p = 0.69
H1: p < 0.69

Here claim is that proportion of overweight people in Bozeman is less than 0.69

c)
SE = sqrt(0.69*0.31/150) = 0.03776
pcap = 87/150 = 0.58

test statistics, z = (0.58 - 0.69)/0.03776 = -2.91313

d)
p-value = 0.00178
As p-value is less than the significance level, we reject the null hypothesis.

e) Reject null hypothesis

f) This means there are significant evidence to conclude that people of Bozeman are healthier

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