A survey of 29 sugar addicts showed that they eat 13 jumbo candy bars a week....

A survey of 29 sugar addicts showed that they eat 13 jumbo candy bars a week. If the trend follows a typical normal distribution with a standard deviation of 3 candy bars a week, find the 99% confidence interval for the true average amount of candy bars eaten per week.

Expert Solution

solution

Given that,

= 13

s =3

n = 29

Degrees of freedom = df = n - 1 =29 - 1 =28

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t /2,df= t0.005,28 = 2.763 ( using student t table)

Margin of error = E = t/2,df * (s / $\sqrt$ n)

= 2.763* (3 / $\sqrt$ 29) = 1.5392

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

- E < < + E

13 - 1.5392< < 13+ 1.5392

11.4608< <14.5392

11.4608,14.5392

orchestra answered 1 year ago

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