Question

In: Statistics and Probability

A survey of 10 smokers showed that they smoke an average of 13 packs. the data...

A survey of 10 smokers showed that they smoke an average of 13 packs. the data follows a normal distribution, with a previous record of standard deviation as 3 packs per week. find the 95% confidence interval for the true average of packs smoked per week.

What is the sample mean value?

Which distribution is used in this case?

What is the Maximal Margin of Error?

What is the confidence interval?

Solutions

Expert Solution

Given,

Sample mean, = 13 packs

Population standard deviation, = 3 packs

Sample size, = 10

We have to construct a 95% confidence interval for the population mean with known standard deviation.

The critical value for α=0.05 is Z​c=1.96.

The margin of error is given by,

  

The corresponding confidence interval is computed as shown below:

Answers:

What is the sample mean value? - 13 packs

Which distribution is used in this case? - Normal distribution ( since standard deviation is known)

What is the Maximal Margin of Error? - 1.8594

What is the confidence interval? - ( 11.1406 , 14..8594)

orchestra answered 1 year ago
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