Respuesta :
Answer:
i. Point of estimate:
[tex] \hat \mu = \bar X =143.0[/tex]
ii. Margin of error:
[tex] ME = 2.01 *\frac{56.7}{\sqrt{50}}= 16.12[/tex]
iii. The 90% confidence interval
Replacing in the confidence interval formula we got
[tex]143.0-16.12=126.88[/tex]
[tex]143.0+16.12=159.12[/tex]
The 90% confidence interval is 126.88 to 159.12
Step-by-step explanation:
Information given
[tex]\bar X=143.0[/tex] represent the sample mean for the variable of interest
[tex]\mu[/tex] population mean
s=56.7 represent the sample standard deviation
n=50 represent the sample size
Confidence interval
The confidence interval for the true mean when we don't know the deviation is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
In order to calculate the critical value for the confidence interval [tex]t_{\alpha/2}[/tex] we need to find the degrees of freedom, with this formula:
[tex]df=n-1=50-1=49[/tex]
The Confidence level provided is 0.90 or 90%, the value for the significance is [tex]\alpha=1-0.9=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,49)".And we see that [tex]t_{\alpha/2}=2.01[/tex]
i. Point of estimate:
[tex] \hat \mu = \bar X =143.0[/tex]
ii. Margin of error:
[tex] ME = 2.01 *\frac{56.7}{\sqrt{50}}= 16.12[/tex]
iii. The 90% confidence interval
Replacing in the confidence interval formula we got
[tex]143.0-16.12=126.88[/tex]
[tex]143.0+16.12=159.12[/tex]
The 90% confidence interval is 126.88 to 159.12
