Question

The average selling price of a smartphone purchased by a random sample of 45 customers was ​$313. Assume the population standard deviation was ​$32.

a. Construct a 95​% confidence interval to estimate the average selling price in the population with this sample.

b. What is the margin of error for this​ interval?

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 313

Population standard deviation =    = 32

Sample size n =45

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 * ( 32 / 45 )

= 9.3
At 95% confidence interval
is,

- E < < + E

313 -9.3 <   < 313 + 9.3

(303.7 , 322.3)

b.

Margin of error = E =   Z/2    * ( /n)
= 1.96 * ( 32 / 45 )

= 9.3