Question

A sample of data is drawn from an unknown population. The sample
size is *n* = 30, with a mean of 21.4, and sample standard
deviation of 7. What is the upper confidence limit (UCL) of the 98%
CI?

Round to two decimals and include leading zeros if necessary.

Answer #1

Solution :

Given that,

= 21.4

s = 7

n = 30

Degrees of freedom = df = n - 1 = 30 - 1 = 29

At 98% confidence level the t is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

t_{ /2,df} =
t_{0.01,29} = 2.462

Margin of error = E = t_{/2,df} * (s /n)

= 2.462 * (7 / 30) = 3.1

The 98% confidence interval estimate of the population mean is,

- E < < + E

21.4 - 3.1 < < 21.4 + 3.1

18.3 < < 24.5

(18.3, 24.5 )

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