Question

In the average month there is about 150,000 trucks sold across the board. There is about 350,000 vehicles sold every month. Trucks make up about 43% of the sales every month in the USA. At a 95% confidence level there are between ____% and ____% trucks sold every month.

Answer 1

Solution :

Given that,

n = 350000

x = 150000

Point estimate = sample proportion = = x / n = 0.43

1 - = 0.57

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.96 * (((0.43 * 0.57) / 350000)

= 0.002

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.43 - 0.002 < p < 0.43 + 0.002

0.428 < p < 0.432

At a 95% confidence level there are between 42.8% and 43.2% trucks sold every month.