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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.

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JeanaShupp

Answer: [tex](3.4,\ 3.6)[/tex]

Step-by-step explanation:

Given : Sample size : n= 1083

The sample mean : [tex]\overline{x}=3.5[/tex]

Standard deviation : s= 1.3

Critical 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]

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