Question

The amounts (in ounces) of juice in eight randomly selected juice bottles are:15.4 15.8 15.4 15.115.8 15.9 15.8 15.7. Construct a 98% confidence interval for the mean amount of juice in all such bottles.

Answer 1

15.33
`\leq`μ
`\leq`15.89

Explanation:

given observations

15.4

15.8

15.4

15.1

15.8

15.9

15.8

15.7.

mean(x)=15.6125

Variance (s2): 0.068593750000048

standard deviation(s)=0.2619040854970537

as we dont know the population standard deviation so we use t-stat

formula

t
`(α )/(2)`,n-1=
}[/tex]}[/tex]

where

s-sample standard deviation

x-sample mean

μ-population mean

n-sample size

x-t×
}[/tex]
`\leq`μ
`\leq` t×
}[/tex]+x

for 98% confidence interval and 7 degrees of freedom

t=2.998

15.33
`\leq`μ
`\leq`15.89 is the 98% confidence interval for mean