Question

2. In 2016, the Centers for Disease Control and Prevention reported that 36.5% of adults in the United
States are obese. A county health service planning a new awareness campaign polls a random sample
of 750 adults living there. In this sample, 228 people were found to be obese based on their answers
to a health questionnaire. Do these responses provide strong evidence that the 36.5% figure is not
accurate for this region? Use a significance level of 5% to test your hypothesis.
a) Define the parameter of interest.
b) State the hypotheses statements.
c) Check that the conditions have been met and name the significance test to be used.
d) Perform the test and show all work.
e) Interpret the P-value and state your conclusion.
f) Calculate and interpret a 95% confidence interval.
g) Describe what a Type I and Type II error would be in the

Answer 1

solution:

sample size = n = 750

number of obese = 228

proportion of obese in the sample = = 228/750 = 0.304

null and alternative hypothesis

c) conditions to be checked :

random sample: it is given that this is a random sample

10% condition: since the sample of 750 is less than the 10% of the total population.

success of failute condition: both success and failure should be atleast 10

np = 750*0.365 = 273.75

n(1-p) = 750*(1-0.365) = 476.25

both are greater than 10

thus all the conditions are satisfied

test statistics:

p value = P(z < -3.47) or P(z > 3.47) because it is a two tailed test

p value = 2 (value of z to the left of -3.47)

p value = 2(0.0003) = 0.0006

since p value = 0.0006 < 0.05, so null hypothesis is rejected

conclusion:

there is sufficient evidence that proves the claim that the proportion of obese is different from the 36.5%

confidence interval =

margin of error =

upper limit of interval = 0.304 + 0.033 = 0.337

lower limit = 0.304 - 0.033 = 0.271

type I error: type I error occured when we reject the null hypothesis when it was actually true.

Type II error: it occurred when we accept the null hypothesis when it was actually false or alternative is true.