Answer :
Answer:
[tex]50-1.64\frac{15}{\sqrt{30}}=45.509[/tex]
[tex]50+1.64\frac{15}{\sqrt{30}}=54.491[/tex]
The 90% confidence inverval for the mean will be 45.509 and 54.491
Step-by-step explanation:
Information given
[tex]\bar X= 50[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma= 15[/tex] represent the sample standard deviation
n= 30 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 0.90 or 90%, the value of [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], the critical value would be [tex]z_{\alpha/2}=1.64[/tex]
Now we have everything in order to replace into formula (1):
[tex]50-1.64\frac{15}{\sqrt{30}}=45.509[/tex]
[tex]50+1.64\frac{15}{\sqrt{30}}=54.491[/tex]
The 90% confidence inverval for the mean will be 45.509 and 54.491