Question 1: In order to get a better understanding of which types of people buy their...

Question 1: In order to get a better understanding of which types of people buy their product, a large company wanted to estimate the proportion of customers who are considered low income. They took a random sample (a very small subset) of 500 customers and found that 210 were low income.

a) Check to see if conditions (there are 4) are met to have a valid confidence interval.

b) What would happen to the distribution of sample proportions if one the first three conditions are not met (sample size conditions)?

c) Construct an approximate 95% confidence interval for the proportion of low-income customers.

d) Interpret the interval found in “c”.
e) Calculate the confidence interval width of the interval created in “c”
f) If were to calculate an 85% confidence interval what z* values would you use? g) What do the values in “f” represent conceptually?
h) Which confidence interval would be more precise (smaller width); 95% or 85%?

i) Before the company took its initial sample (They did not take the 500 observation sample yet), they ideally wanted to have a confidence interval width of 0.048 when creating an approximate 95% confidence interval. What is the least amount of people they needed to sample in order to guarantee there confidence interval width would not be larger than 0.048.

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Expert Solution

orchestra answered 1 year ago

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