Suppose you randomly sample 64 cans and find the mean amount of Coke in this sample...

Suppose you randomly sample 64 cans and find the mean amount of Coke in this sample is 11.85 ounces and the standard deviation is 0.35 ounces. Construct a 95% confidence interval estimate for the mean amount of Coke in the all such cans.

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Expert Solution

Solution :

Given that,

$\bar x$ = 11.85

$\sigma$ = 0.35

n = 64

At 95% confidence level the z is ,

$\alpha$ = 1 - 95% = 1 - 0.95 = 0.05

$\alpha$ / 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Margin of error = E = Z_/2* ( $\sigma$ / $\sqrt$ n)

= 1.96* (0.35 / $\sqrt$ 64)

= 0.09 (rounded)

At 99% confidence interval estimate of the population mean is,

$\bar x$ - E < $\mu$ < $\bar x$ + E

11.85-0.09 < $\mu$ < 11.85+0.09

11.76< $\mu$ < 11.94

orchestra answered 2 years ago

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