Question

A market surveyor wishes to know how many energy drinks teenagers drink each week. They want to construct a 80% confidence interval for the mean and are assuming that the population standard deviation for the number of energy drinks consumed each week is 1. The study found that for a sample of 256 teenagers the mean number of energy drinks consumed per week is 4.7. Construct the desired confidence interval. Round your answers to one decimal place.

Answer 1

The 80% confidence interval for the mean

(4.6199 , 4.7801)

Explanation:

Explanation:-

Assuming that the population standard deviation for the number of energy drinks consumed each week is 1

Given the Population standard deviation 'σ' = 1

The study found that for a sample of 256 teenagers the mean number of energy drinks consumed per week is 4.7

given sample size 'n' = 256

mean of the sample 'x⁻' = 4.7

confidence interval for the mean

The 80% confidence interval for the mean is determined by

`(x^(-) -Z_(\alpha ) (S.D)/(√(n) ) , x^(-) + Z_(\alpha )(S.D)/(√(n) ) )`

the z-score of 80% level of significance = 1.282

`(4.7 - 1.282(1)/(√(256) ) , 4.7 + 1.282(1)/(√(256) ) )`

(4.7 - 0.0801 , 4.7 +0.0801)

(4.6199 , 4.7801)

Conclusion:-

The 80% confidence interval for the mean

(4.6199 , 4.7801)