Answer:
[tex]46816-1.695\frac{12557}{\sqrt{651}}=45981.81[/tex]
[tex]46816+ 1.695\frac{12557}{\sqrt{651}}=46650.19[/tex]
And the confidence interval would be given by: (45981.81; 46650.19)
Step-by-step explanation:
Data given
[tex]\bar X=46816[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma=12557[/tex] represent the population standard deviation
n=651 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
Since the Confidence is 0.91 or 91%, the significacne is [tex]\alpha=0.09[/tex] and [tex]\alpha/2 =0.045[/tex], and the critical value is [tex]z_{\alpha/2}=1.695[/tex]
Now we have everything in order to replace into formula (1):
[tex]46816-1.695\frac{12557}{\sqrt{651}}=45981.81[/tex]
[tex]46816+ 1.695\frac{12557}{\sqrt{651}}=46650.19[/tex]
And the confidence interval would be given by: (45981.81; 46650.19)
