a sample of 57 observations for alcohol levels randomly taken on highway 6 at 3am on saturday, resulted in a mean of 0.057 and a variance of 0.0075 respectively. construct a 99% confidence interval on the population mean alcohol level in this situation.

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19-12-2022
Mathematics

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a sample of 57 observations for alcohol levels randomly taken on highway 6 at 3am on saturday, resulted in a mean of 0.057 and a variance of 0.0075 respectively. construct a 99% confidence interval on the population mean alcohol level in this situation.

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ankit362097kumar ankit362097kumar · Answer 1 · 2022-12-23T01:45:33-05:00

A 99% confidence interval on the population mean alcohol level in this situation is 0.0347.

A sample of 57 observations for alcohol levels randomly taken on highway 6 at 3am on Saturday, resulted in a mean of 0.057 and a variance of 0.0075 respectively.

n= 57

x=0.037

σ[tex]^{2}[/tex] = 0.0001099

σ = √σ2

=√0.0001099

σ = 0.01048

90% confidence interval,

d= 1-0.9=0.1

From z-table, [tex]z_{\frac{2}{z} }=z_{0.05}=1.645[/tex]

90% confidence interval,

δ= x±[tex]z_{\frac{\alpha }{2} }[/tex].σ/√n

= 0.037±1.645×[tex]\frac{0.01048}{\sqrt{57} }[/tex]

= [tex]0.037[/tex]±0.0023

= (0.0347, 0.0393)

Lower limit = 0.0347

Upper limit = 0.0393

Therefore, the lower limit is 0.347.

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