Question

The mean number of hours of part-time work per week for a sample of 317 teenagers is 29. If the margin of error for the population mean with a 95% confidence interval is 2.1, construct a 95% confidence interval for the mean number of hours of part-time work per week for all teenagers.

Answer 1

Answer:

The degrees of freedom are given by:

$df=n-1=317-1=316$

And replaicing we got:

$29-2.1=26.9$    

$29+2.1=31.1$    

The 95% confidence interval would be between 26.9 and 31.1

Step-by-step explanation:

Information given

$\bar X= 29$ represent the sample mean

$\mu$ population mean

s represent the sample standard deviation

$ME= 2.1$ represent the margin of error

n represent the sample size  

Solution

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$   (1)

And this formula is equivalent to:

$\bar X \pm ME[/te]xThe degrees of freedom are given by:[tex]df=n-1=317-1=316$

And replaicing we got:

$29-2.1=26.9$    

$29+2.1=31.1$    

The 95% confidence interval would be between 26.9 and 31.1