Question

Calculate the upper and lower limit for a 95% confidence interval about the mean.

A family wants to reduce its expenditures for personal items like gifts, newspapers, magazines and so forth. A sample of 49 months of receipts yields a mean of $220.00 with a standard deviation of $30.00. They decide to calculate a 95% confidence interval about this mean.

Answer 1

Upper limit (dollars and cents) $228.40.
Lower limit (dollars and cents) $211.60.

Hope this helps.

Answer 2

`(\$228.41,\$211.59)`

Explanation:

Confidence interval would be,

`=\overline{X}\pm Z(s)/(√(n))`

Where,

`\overline{X}` = mean = 220

Z = z score of the confidence interval = 1.96 (for 95% confidence interval)

s = standard deviation = 30

n = sample size = 49

Putting the values,

`=220\pm 1.96\left((30)/(√(49))\right)`

`=220\pm 1.96\left((30)/(7)\right)`

`=220\pm 1.96\left(4.29\right)`

`=220\pm 8.41`

`=220+8.41,220- 8.41`

`=228.41,211.59`