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.

Expert Solution

orchestra answered 2 years ago

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