##### Question

In: Statistics and Probability

# Construct a 95?% confidence interval to estimate the population mean using the following data. What assumptions...

Construct a 95?% confidence interval to estimate the population mean using the following data. What assumptions need to be made to construct this? interval?

 x?=93 ?=15 n=17

With 95?% ?confidence, when n=17 the population mean is between the lower limit of __ and the upper limit of __

## Solutions

##### Expert Solution

Solution :

Given that,

= 93

= 15

n = 17

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

Margin of error = E = Z/2* ( /$\sqrt$n)

=1.96 * (15 / $\sqrt$17)

= 7.1305

At 99% confidence interval estimate of the population mean is,

- E < < + E

93-7.1305 < < 93+7.1305

85.8695< < 100.1305

With 95?% ?confidence, when n=17 the population mean is between the lower limit of 85.8695 and the upper limit of 100.1305

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