What proportion of female college students in the USA use social media? Let p be
ID: 3235779 • Letter: W
Question
What proportion of female college students in the USA use social media? Let p be the (unknown) true proportion of female college students in the USA who use social media. In a random sample of n = 2500 female college students, 2050 said they use social media.
a)Obtain an unbiased point estimate of p. 1
b) We wish to construct a 90 % classical confidence interval for p. What is the critical value multiplier zstar? 2
c) Create a 90% classical confidence interval for p?
3 , 4
d) How long is the 90% classical confidence interval for p? 5
e) In terms of p and n, give the formula for the standard deviation of the distribution of the sample proportion of female college students who use social media (R code OK) 6
f) Based on this data and the formula in part e, estimate the standard deviation of the sample proportion of female college students who use social media. (4 digits of accuracy (4 digits of accuracy) 7
g) Copy your R script for the above into the text box here.
8
Explanation / Answer
What proportion of female college students in the USA use social media? Let p be the (unknown) true proportion of female college students in the USA who use social media. In a random sample of n = 2500 female college students, 2050 said they use social media.
a)Obtain an unbiased point estimate of p. = p^ = (2050)/ 2500 = 0.82
(b) We wish to construct a 90 % classical confidence interval for p. What is the critical value multiplier zstar?
Zstar for 90% confidence interval = +- 1.645
(c) Standard error of the proportion se0 = sqrt [ p^(1-p^)/N] = Sqrt [0.82 * 0.18/2500] = 0.00768
Create a 90% classical confidence interval for p = p^ +- Z90% se0
= 0.82 +- 1.645 * 0.00768 = (0.8074, 0.8326)
(d) Length of 90% CI = 0.8326 - 0.8074 = 0.0252
(e) standard deviation of the distribution of the sample proportion of female college students who use social media = sqrt [p(1-p)/n]
(f) estimate the standard deviation of the sample proportion of female college students who use social media.
= sqrt [ 0.82 * 0.18/ 2500] = 0.00768
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