Question

A simple random sample of 50 items from a population with 7 resulted in a sample mean of 35.

Answer 1

The 90% , 99% confidence interval for the population mean is 32.145 < $\rm \mu$ < 35.855 and 31.093 <  $\rm \mu$ < 36.907

What is Probability ?

Probability is the study of likeliness of an event to happen.

It is given that

Total Population = 50

Mean = 35

The confidence interval is given by

$\rm CI = \mu + z \dfrac{s}{\sqrt n}$

$\rm \mu$ is the mean

z is the confidence level value

s is the standard deviation

n is the population width

(a) The 90% confidence interval for the population mean

90% $\rm \alpha / 2$  = 0.05

Z = 1.64

34 $\rm \pm$ 1.64 * 8 / √50

34 $\rm \pm$  1.855

32.145 < $\rm \mu$ < 35.855

(b)  The 99% confidence interval for the population mean

99% $\rm \alpha / 2$  = 0.005

Z=2.57

34  $\rm \pm$ 2.57 * 8 / √50

34 $\rm \pm$  2.907

31.093 <  $\rm \mu$ < 36.907

Therefore the confidence interval for population mean has been determined.

The complete question is

A simple random sample of 50 items from a population width =7  resulted in a sample mean of 35. If required, round your answers to two decimal places.

a. Provide a 90% confidence interval for the population mean

b. Provide a 99% confidence interval for the population mean

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