B) standard error PLEASE :) A survey of 350 students is selected randomly on a l
ID: 3156701 • Letter: B
Question
B) standard error PLEASE :)
A survey of 350 students is selected randomly on a large university campus. They are asked if they use a laptop in class to take notes. Suppose that based on the survey 210 of the 350 students responded "yes." What is the value of the sample proportion p? What is the standard error of the sample proportion? Construct an approximate 95% confidence interval for the true proportion p by taking plusminus 2 SEs from the sample proportion. p (Type an integer or a decimal.) The standard error of the sample proportion is (Round to three decimal places as needed.) The approximate 95% confidence interval for the true proportion p by taking plusminus 2 SEs from the sample proportion is (Round to three decimal places as needed.)Explanation / Answer
The mean of the distribution of sample proportions is equal to the population proportion, p. If p is unknown, we estimate it using pˆ. The standard deviation of the distribution of sample proportions is symbolized by SE(pˆ) and equals sqrt((p(1-p)/n)this is the standard error of pˆ. The symbol pˆis also used to signify the standard deviation of the distirbution of sample proportions.
Here p =0.6 and n=350
Hence standard error =sqrt((p(1-p)/n)=sqrt(0.6*0.4/350)=0.02619
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