Respuesta :
Answer:
[tex]9797-1.67\frac{2313}{\sqrt{61}}=9302.43[/tex]
[tex]9797+1.67\frac{2313}{\sqrt{61}}=10291.57[/tex]
And we can conclude that at 90% of confidence the true mean for the number of steps taken on a typical workday for all people working in New York City who wear an activity tracker is between 9302.43 and 10291.57
Step-by-step explanation:
Data provided
[tex]\bar X=9797[/tex] represent the sample mean for the steps
[tex]\mu[/tex] population mean
s=2313 represent the sample standard deviation
n=61 represent the sample size
Solution
The confidence interval for the true population mean is given by :
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
Since we need to find the critical value [tex]t_{\alpha/2}[/tex] we need to calculate first the degrees of freedom, given by:
[tex]df=n-1=61-1=60[/tex]
The Confidence is 0.90 or 90%, the value for the significance is [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,60)".And we see that [tex]t_{\alpha/2}=1.67[/tex]
Now we have everything in order to replace into formula (1):
[tex]9797-1.67\frac{2313}{\sqrt{61}}=9302.43[/tex]
[tex]9797+1.67\frac{2313}{\sqrt{61}}=10291.57[/tex]
And we can conclude that at 90% of confidence the true mean for the number of steps taken on a typical workday for all people working in New York City who wear an activity tracker is between 9302.43 and 10291.57
