Answer:
[tex]3.20-1.304\frac{0.8}{\sqrt{40}}=3.035[/tex]
[tex]3.20+1.304\frac{0.8}{\sqrt{40}}=3.365[/tex]
And the confidence interval would be between (3.035;3.365)
Step-by-step explanation:
Information given
[tex]\bar X=3.20[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s=0.8 represent the sample standard deviation
n=40 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=40-1=39[/tex]
The Confidence level is 0.80 or 80%, the significance would be [tex]\alpha=0.2[/tex] and [tex]\alpha/2 =0.1[/tex], and the critical value would be [tex]t_{\alpha/2}=1.304[/tex]
Now we have everything in order to replace into formula (1):
[tex]3.20-1.304\frac{0.8}{\sqrt{40}}=3.035[/tex]
[tex]3.20+1.304\frac{0.8}{\sqrt{40}}=3.365[/tex]
And the confidence interval would be between (3.035;3.365)
