Respuesta :
Answer:
(88.6, 245.4)
Step-by-step explanation:
Given that suppose you obtained a mean of $167 spent on transportation and a standard deviation of $40.
We are to calculate a 95% confidence interval for the mean
Assuming normal distribution we say critical value for 95% is 1.96
Margin of error = 1.96(std deviation)
= 78.40
Confidence interval = (Mean-margin of error, Mean + margin of error)
= (167-78.4, 167+78.4)
= (88.6, 245.4)
Answer:
95% confidence interval for the mean = [88.6 , 245.4]
Step-by-step explanation:
We are given that a mean of $167 spent on transportation and a standard deviation of $40 is obtained.
We have to calculate a 95% confidence interval for the mean.
The 95% confidence interval formula for mean rate is given by;
95% confidence interval for [tex]\mu[/tex] = Sample mean [tex]\pm[/tex] [tex]Z_\frac{\alpha}{2}[/tex] * Standard deviation
Here, sample mean = $167
standard deviation = $40
[tex]Z_\frac{\alpha}{2}[/tex] = critical value of Z at [tex]\alpha[/tex] (significance level) of 5% is given in z table
as 1.96 .
So, 95% confidence interval for [tex]\mu[/tex] = [167 - (1.96 * 40) , 167 + (1.96 * 40)]
= [ 167 - 78.4 , 167 + 78.4 ]
= [88.6 , 245.4]
