Question

A report from the U.S. Department of Agriculture shows that the mean American consumption of carbonated beverages per year is greater than 52 gallons. A random sample of 30 Americans yielded a sample mean of 69 gallons. Assume that the population standard deviation is 20 gallons, and the consumption of carbonated beverages per year follows a normal distribution. Calculate a 95% confidence interval, and write it in a complete sentence related to the scenario.

Answer 1

Solution :

Given that,

= 69

= 20

n = 30

At 95% confidence level the z is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.960

Margin of error = E = Z_/2* (/n)

= 1.960 * (20 / 30  )

= 7.16

At 95% confidence interval estimate of the population mean is,

- E < < + E

69 - 7.16 < < 69 + 7.16

61.84 < < 76.16

American consumption of carbonated beverages per year is greater than 52 gallons.

The consumption of carbonated beverages per year between 61.84 gallons. and  76.16 gallons.