Answer:
The answer is below
Step-by-step 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:
[tex]E = z_\frac{\alpha}{2} *\frac{\sigma}{\sqrt{n} } \\\\E=1.65*\frac{0.7}{\sqrt{50} } =0.16[/tex]
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
