The next questions are related: According to centers for Disease Control and Pre

Question

The next questions are related:

According to centers for Disease Control and Prevention, 31.2% of the adult population in the Midwest are obese ( = 0.312). In random samples of n = 600 Midwestern adults, the standard error of the sample proportion is:
a 0.0151 b 0.0189 c 0.0227 d 0.0284
In the previous question, what fraction of sample proportions from samples of size n = 600 exceed 0.34?
a 0.0694 b 0.0833 c 0.0917 d 0.1008 We want to build a middle interval which captures 95% of all sample proportions within ±0.03 from the population proportion of adults who are obese. What is the minimum
sample size to build this interval?
a 1064 b 982 c 917 d 871 The next questions are related:

According to centers for Disease Control and Prevention, 31.2% of the adult population in the Midwest are obese ( = 0.312). In random samples of n = 600 Midwestern adults, the standard error of the sample proportion is:
a 0.0151 b 0.0189 c 0.0227 d 0.0284
In the previous question, what fraction of sample proportions from samples of size n = 600 exceed 0.34?
a 0.0694 b 0.0833 c 0.0917 d 0.1008 We want to build a middle interval which captures 95% of all sample proportions within ±0.03 from the population proportion of adults who are obese. What is the minimum
sample size to build this interval?
a 1064 b 982 c 917 d 871

Explanation / Answer

a) Standard error will be = sqrt(0.312*(1-0.312)/600) = 0.0189

correct option is B

b) Sample proportions exceed 0.34

Z = (0.34-0.312)/0.0189 = 1.4803

1-NORMSDIST(1.4803) = 0.0694

Correct option is A

c) Critcal value at 95% interval will be 1.960

Minimum sample size will be = ((1.960/0.03)^2)*0.312*(1-0.312) = 917 (nearest integer)

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