Question

The 90% confidence interval for the mean one-way commuting time in New York City is 37.8 < μ < 38.8 minutes. Construct a 95% interval based on the same data. Which interval provides more information.

Answer 1

For the 90% confidence interval the following equations can be formed:
\[37.8=sample\ mean-1.645\frac{\sigma}{\sqrt{n}}\ ...........(1)\]
\[38.8=sample\ mean+1.645\frac{\sigma}{\sqrt{n}}\ ............(2)\]
By adding equations (1) and (2) you can calculate the sample mean and then
\[\frac{\sigma}{\sqrt{n}}\]

Answer 2

So 37.8+38.8=76.6 would the sample mean?

Answer 3

@kropot72 So 37.8+38.8=76.6 would the sample mean?

Answer 4

You need to add the right hand sides of equations (1) and (2) as well as the left hand sides.

Answer 5

@kropot72 so I have to find the standard deviation and the square root of the number first?

Answer 6

You need to find the sample mean and the fraction
\[\frac{\sigma}{\sqrt{n}}\]
You do not need to know sigma and the square root of n (sample size) separately.

Answer 7

@kropot72 I am so confused. How can I add
37.8=sample mean−1.645σ/√n ...........(1)
38.8=sample mean+1.645σ/√n ............(2)
if I do not know the values that I need?

Answer 8

Sorry for delay. My broadband had a fault.
Adding (1) and (2) gives:
\[37.8+38.8=(sample\ mean)+(sample\ mean)-1.645\frac{\sigma}{\sqrt{n}}+1.645\frac{\sigma}{\sqrt{n}}\ ..........(3)\]

Answer 9

Simplifying gives:
76.6 = 2 * (sample mean)
sample mean = 76.6/2
If you now substitute the value just obtained for the sample mean into equation (1) you can find the value of the fraction
\[\frac{\sigma}{\sqrt{n}}\]
Then it becomes possible to construct a 95% confidence interval.