Question

A marketing company wants to know the mean price of new vehicles sold in an up-and‑coming area of town. Marketing strategists takes a simple random sample of 756 cars, and find that the sample has a mean of $27,400 and a standard deviation of $1300.

1. Assume that the population standard deviation is unknown. What is the error of estimate for a 95% confidence interval?

2. Assume that the population standard deviation is known to be $1500. What is the upper bound for a 98% confidence interval?

3. Assume that the population standard deviation is known to be $1500. Find the error of estimate for a 99% confidence interval.

4. Assume that the population standard deviation is known. If the marketing strategists want the 90% confidence interval to be within $50 of the population mean, how many cars at minimum should they sample?

Answer 1

ANSWER::

1Q)
Given that,

Point estimate = sample mean =     = 27400

Population standard deviation =    = 1300

Sample size n =756

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E =   Z/2    * ( /n)
= 1.96* ( 1300/ 756 )

= 93

2Q)

3Q)

4Q)

Given that,

standard deviation =s =   =1300

Margin of error = E = 50

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645

sample size = n = [Z/2* / E] 2

n = ( 1.645 * 1300 / 50 )2

n =1829

Sample size = n =1829

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