Respuesta :
Answer:
[tex]157.3-1.96\frac{15.6}{\sqrt{234}}=155.301[/tex]
[tex]157.3+1.96\frac{15.6}{\sqrt{234}}=159.299[/tex]
So on this case the 95% confidence interval would be given by (155.301;159.299)
And the best option would be:
B. (155.3, 159,3)
Step-by-step explanation:
Information given
[tex]\bar X=157.3[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma =15.6[/tex] represent the population standard deviation
n=234 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)
The Confidence level is is 0.95 or 95%, the significance is [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], the critical value for this case would be [tex]z_{\alpha/2}=1.96[/tex]
And replacing we got:
[tex]157.3-1.96\frac{15.6}{\sqrt{234}}=155.301[/tex]
[tex]157.3+1.96\frac{15.6}{\sqrt{234}}=159.299[/tex]
So on this case the 95% confidence interval would be given by (155.301;159.299)
And the best option would be:
B. (155.3, 159,3)
