Question

Find a 90% confidence interval estimate of the mean weight of all women based on a sample of 35 women with a mean sample weight of 150.27. The standard deviation of all women is known to be 30.87. Write your answer in interval form, using values rounded to two decimals.

Answer 1

The 90% confidence interval of the sample is (140.04,160.5).

Solution-

Assuming it as normal distribution,

Number of observations n = 35

Mean = X = 150.27

Standard Deviation = s = 30.87

Then Confidence Interval we want: 95%, Then the Z value for that Confidence Interval is Z = 1.960

Using that Z in this formula for the Confidence Interval,

`\overline{X}\ \pm \ Z(S)/(√(n) )`

Putting all the values,

`150.27 \pm \ 1.96(30.87)/(√(35)) = 150.27 \pm 10.23 = (140.04,160.5)`