According to a recent study, 68% of adults say they play games on their smartphone. Suppose...
According to a recent study, 68% of adults say they play games on their smartphone.
Suppose we randomly select 200 adults and find that 80% of the sample plays games on
their smartphone. Which of the following correctly describes the distribution for the
proportion of adults in the sample who play games on their smartphone?
A. pˆ ~ AN(0.68, 0.0283)
B. pˆ ~ AN(0.68, 0.0330)
C. X ~ AN(160, 5.6569)
D. pˆ ~ AN(0.80, 0.0283)
Homework Answers
Answer: B. pˆ ~ AN(0.68, 0.0330)
Solution:
We are given
n = 200
p = 0.68
q = 1 - 0.68 = 0.32
Estimate for mean for sampling distribution of sample proportion µp̂ = p = 0.68
µp̂ = 0.68
Estimate for standard deviation for sampling distribution of sample proportion σp̂ is given as below:
σp̂ = sqrt(pq/n) = sqrt(0.68*0.32/200) = 0.032985
σp̂ = 0.033
Answer:
B. pˆ ~ AN(0.68, 0.0330)
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