Respuesta :
The 90% , 99% confidence interval for the population mean is 32.145 < [tex]\rm \mu[/tex] < 35.855 and 31.093 < [tex]\rm \mu[/tex] < 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
[tex]\rm CI = \mu + z \dfrac{s}{\sqrt n}[/tex]
[tex]\rm \mu[/tex] 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% [tex]\rm \alpha / 2[/tex] = 0.05
Z = 1.64
34 [tex]\rm \pm[/tex] 1.64 * 8 / √50
34 [tex]\rm \pm[/tex] 1.855
32.145 < [tex]\rm \mu[/tex] < 35.855
(b) The 99% confidence interval for the population mean
99% [tex]\rm \alpha / 2[/tex] = 0.005
Z=2.57
34 [tex]\rm \pm[/tex] 2.57 * 8 / √50
34 [tex]\rm \pm[/tex] 2.907
31.093 < [tex]\rm \mu[/tex] < 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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