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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.

Respuesta :

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

Hope this helps.
InesWalston

Answer:

[tex](\$228.41,\$211.59)[/tex]

Step-by-step explanation:

Confidence interval would be,

[tex]=\overline{X}\pm Z\dfrac{s}{\sqrt{n}}[/tex]

Where,

[tex]\overline{X}[/tex] = 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,

[tex]=220\pm 1.96\left(\dfrac{30}{\sqrt{49}}\right)[/tex]

[tex]=220\pm 1.96\left(\dfrac{30}{7}\right)[/tex]

[tex]=220\pm 1.96\left(4.29\right)[/tex]

[tex]=220\pm 8.41[/tex]

[tex]=220+8.41,220- 8.41[/tex]

[tex]=228.41,211.59[/tex]

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