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 JJ 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 JJ 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?

Explanation / Answer

a)

0.609

b)

2.054

c)

Normal approximation to the binomial calculation:

Standard error of the mean = SEM = x(N-x)/N3 = 0.044

= (1-CL)/2 = 0.020

Standard normal deviate for = Z = 2.054

Proportion of positive results = P = x/N = 0.610

Lower bound = P - (Z*SEM) = 0.519

Upper bound = P + (Z*SEM) = 0.700

d)

22.26

PS: We are directed to solve only first 4 parts of a question if multi part question is posted

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