How bad is the wireless network at JJ Out of a random sample of 123 JJ students,

Question

How bad is the wireless network at JJ Out of a random sample of 123 JJ students, 75 students said they had a network connection at J3 lost in the past month. Let p be the (unknown) true proportion JJ students who have lost a network connection in the last month. Let phat be the sample proportion a)Obtain an unbiased point estimate of p. b) We wish to construct a 96 % classical confidence interval for p. what is the critical value multiplier zstar? c) Create a 96% classical confidence interval for p? ( , d) How long is the 96% classical confidence interval for p? f) Based on this data estimate the standard deviation of the sample proportion of J3 students who lost a connection in the last month. g)Assuming the same value of the sample proportion what is the smallest sample size for which the length of the 96% confidence interval for p is less than or equal to .12? h) Copy your R script for the above into the text box here.

Explanation / Answer

(a) Unbiased point estmate p^ = 75/123 = 0.61

(b) for 96% confidence interval Z (critical ) = 2.054

(C) 96% classical confidence interval = p^ +- Z96% sqrt [0.61 * 0.39/123]

= 0.61 +- 2.054 * 0.044

= (0.52, 0.70)

(D The width of 96% confidence interval = 0.70 - 0.52 = 0.18

(E) standard deviation of sample proportion = sqrt (0.61 * 0.39/123) = 0.044

(F) Here length of confidence interval < 0.12

Margin of error < 0.06

Critical test statistic * standard error of proportion < 0.06

Z96% sqrt [0.61 * 0.39/n] < 0.06

2.054 * sqrt [0.61 * 0.39/n]< 0.06

sqrt(n) > 2.054 * sqr (0.61 * 0.39)/0.06

n > 278.80

n = 279

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