Question

Question 1.

A) In a simple random sample of 100 graduates from a certain college, 48 were earning $50,000 a year or more. Estimate a 90% confidence interval for the proportions of all graduates of that college earning $50,000 a year or more.

A box contains a large number of red and blue tickets; the proportion of red tickets is known to be 50%. A simple random sample of 100 tickets is drawn from the box. Say whether each of the following statements is true or false, and explain briefly.

a. The percentage of red tickets in the sample has an expected value of 50% and an SE of 5%.

b. The 5% measures the likely size of the chance error in the 50%.

c. The proportion of reds in the sample will be around 50%, give or take 5% or so.

d. An approximate 95%-confidence interval for the proportion of reds in the sample is 40% to 60%.

e. There is about a 95% chance that the proportion of reds in the sample will be in the range from 40% to 60%.

Answer 1

In a simple random sample of 100 graduates from a certain college, 48 were earning $50,000 a year or more. Estimate a 90% confidence interval for the proportions of all graduates of that college earning $50,000 a year or more.

solution:

here =x/n = 48/100=0.48

std error,SE = sqrt (1-)/n =sqrt (0.48*0.52/100)=0.04996

90% confidence interval-

Zalpha/2 = Z_0.10/2=0.05 = 1.645

CI = +/-Z*SE = 0.48+/-1.645*0.04996 =0.48+/-0.082184

so, 90% confidenc interval is

{0.398,0.562}

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