Question

When you fill your coffee at a gas station, you're supposed to get 8 ounces of coffee with a standard deviation of .7 ounces. A random sample of 50 "8 ounce" coffees is collected and measured and the mean was found to be 7.8 ounces.

Answer 1

The answer is below

Explanation:

When you fill your coffee at a gas station, you're supposed to get 8 ounces of coffee with a standard deviation of .7 ounces. A random sample of 50 "8 ounce" coffees is collected and measured and the mean was found to be 7.8 ounces. a) Find a 90% confidence interval. b) Interpret the confidence interval in the context.

Solution:

The confidence = 90% = 0.9, mean (μ) = 7.8 ounces, standard deviation (σ) = 0.7 ounces, sample size (n) = 50

α = 1 - C = 1 - 0.9 = 0.1

α/2 = 0.1 / 2 = 0.05

The z score of α/2 is the same as the z score of 0.45 (0.5 - 0.05) which is equal to 1.65

The margin of error (E) is given by:

`E = z_(\alpha)/(2) *(\sigma)/(√(n) ) \\\\E=1.65*(0.7)/(√(50) ) =0.16`

The confidence interval = μ ± E = 7.8 ± 0.16 = (7.64, 7.96)

b) This means that we are 90% confident that any selected coffee has a weight between 7.64 ounce to 7,96 ounce