PLEASE SHOW ALL WORK. Imagine that you are interested in the average income of t

Question

PLEASE SHOW ALL WORK.

Imagine that you are interested in the average income of the fathers of out-of-state students at the university. You suspect that their income ranges from $60,000 to $300,000. You have decided to use a survey to determine this information but you are unsure of how many people to include in your sample. This information is important for your project so you want to estimate the income within $10,000 of the true value of the population.

What sample size would you recommend if you used a 95% confidence level (Z = 1.96)?

If you only expected a 10% response rate, how many total people would you need to send your survey to?

If you decided that you wanted to be twice as precise in your estimate, what would happen to the sample size you calculated in (a)? Note: you do not need to recalculate n. Indicate if it would increase or decrease.

Explanation / Answer

here std deviation of income from uniform distribution =(b-a)/(12)1/2 =(300000-60000)/(!2)1/2 =69282.03

for z=1.96

margin of errorr E=10000

hence sample size =(z*std deviaiton/E)2 =~185

b) fore response rate 10%, sample size=185/0.1=1850

c) it will increase as more precision means less margin of error which is inversely proportional to sample size

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