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.

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TickinTock TickinTock · Answer 1 · 2017-02-09T12:47:41-05:00

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

Hope this helps.

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InesWalston InesWalston · Answer 2 · 2018-12-06T07:34:12-05:00

Answer:

$(\$228.41,\$211.59)$

Step-by-step explanation:

Confidence interval would be,

$=\overline{X}\pm Z\dfrac{s}{\sqrt{n}}$

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,

$=220\pm 1.96\left(\dfrac{30}{\sqrt{49}}\right)$

$=220\pm 1.96\left(\dfrac{30}{7}\right)$

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

$=220\pm 8.41$

$=220+8.41,220- 8.41$

$=228.41,211.59$