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.
Accepted Solution
A:
Answer: [tex](3.4,\ 3.6)[/tex]Step-by-step explanation:Given : Sample size : n= 1083The sample mean : [tex]\overline{x}=3.5[/tex]Standard deviation : s= 1.3Critical value for 90% confidence interval : [tex]z_{\alpha/2}=1.645[/tex]Confidence interval for population mean is given by :-[tex]\overline{x}\pm z_{\alpha/2}\dfrac{s}{\sqrt{n}}[/tex][tex]3.5\pm (1.645)\dfrac{1.3}{\sqrt{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)[/tex] [Rounded to one decimal place.]Hence, the required confidence interval : [tex](3.4,\ 3.6)[/tex]