Respuesta :
Answer:
[tex]2169.67-2.624\frac{48.72}{\sqrt{15}}=2136.66[/tex]
[tex]2169.67+2.624\frac{48.72}{\sqrt{15}}=2202.68[/tex]
And the confidence interval would be given by (2137, 2203)
Step-by-step explanation:
2051 ,2061 ,2162 ,2167 , 2169 ,2171 , 2180 , 2183 , 2186 , 2195 , 2196 , 2198 , 2205 , 2210 ,2211
We can calculate the mean and deviation with these formulas:
[tex]\bar X= \sum_{i=1}^n \frac{x_i}{n}[/tex] (2)
[tex]s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}[/tex] (3)
And we got:
[tex]\bar X=2169.67[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean
s=48.72 represent the sample standard deviation
n=15 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=15-1=14[/tex]
Since the Confidence is 0.98 or 98%, the significance is [tex]\alpha=0.02[/tex] and [tex]\alpha/2 =0.01[/tex], and using excel we calculate the critical value [tex]t_{\alpha/2}=2.624[/tex]
Now we have everything in order to replace into formula (1):
[tex]2169.67-2.624\frac{48.72}{\sqrt{15}}=2136.66[/tex]
[tex]2169.67+2.624\frac{48.72}{\sqrt{15}}=2202.68[/tex]
And the confidence interval would be given by (2137, 2203)
