Question

The average selling price of a smartphone purchased by a random sample of 40 customers was $308. Assume the population standard deviation was $30. Using a 95​% confidence interval to estimate the average selling price in the population ranges from $298.70 to $313.70.

Question 3 options:

True

False

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 308

Population standard deviation =    = 30

Sample size n =40

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* (30 / 40 )

= 9.30
At 95% confidence interval
is,

- E < < + E

308 - 9.30 <   < 308 + 9.30

298.7 <   < 317.3

yes this is true

95​% confidence interval to estimate the average selling price in the population ranges from $298.70 to $313.70.