Question

A market research company wishes to know how many energy drinks adults drink each week. They want to construct a 90% confidence interval for the mean and are assuming that the population standard deviation for the number of energy drinks consumed each week is 1.3. The study found that for a sample of 1083 adults the mean number of energy drinks consumed per week is 3.5. Construct the desired confidence interval. Round your answers to one decimal place.

Answer 1

Answer:
`(3.4,\ 3.6)`

Explanation:

Given : Sample size : n= 1083

The sample mean :
`\overline{x}=3.5`

Standard deviation : s= 1.3

Critical value for 90% confidence interval :
`z_(\alpha/2)=1.645`

Confidence interval for population mean is given by :-

`\overline{x}\pm z_(\alpha/2)(s)/(√(n))`

`3.5\pm (1.645)(1.3)/(√(1083))\\\\=3.5\pm0.0649822921401\\\\=3.5\pm0.06\\\\=(3.5-0.06,\ 3.5+0.06)\\\\=(3.44,\ 3.56)\approx(3.4,\ 3.6)` [Rounded to one decimal place.]

Hence, the required confidence interval :
`(3.4,\ 3.6)`