help with statistics!

We would like to estimate the true mean amount of time (in minutes) Canadian teenagers spend on the internet per day. The population standard deviation of daily internet usage time is known to be 36 minutes.

(a) What sample size is required in order to estimate to within 15 minutes with 95% confidence?

Question

help with statistics!

We would like to estimate the true mean amount of time (in minutes) Canadian teenagers spend on the internet per day.  The population standard deviation of daily internet usage time is known to be 36 minutes.

(a)  What sample size is required in order to estimate  to within 15 minutes with 95% confidence?

bambimonster · Answer

see attachment if needed

bambimonster · Answer

@kropot72

kropot72 · Answer

The confidence interval must be 30 minutes to estimate within plus/minus 15 minutes.$$\bar{x}+1.960\frac{\sigma}{\sqrt{n}}-(\bar{x}-1.960\frac{\sigma}{\sqrt{n}})=30\ .........(1)$$
Simplifying equation (1) gives
$$3.92\frac{\sigma}{\sqrt{n}}=30$$
Plugging in the value for sigma and rearranging we get
$$\sqrt{n}=\frac{3.92\times36}{30}$$
and finally
$$n=(\frac{3.92\times39}{30})^{2}$$

bambimonster · Answer

does it mean i will have to find marginal error which is equation 1 first? im confused with this part..

bambimonster · Answer

@kropot72

bambimonster · Answer

@ybarrap

bambimonster · Answer

hey i got 22. but it says wrong

kropot72 · Answer

Try rounding up to a sample size of 23 teenagers. 22 is less than the mixed number given by the calculation.

bambimonster · Answer

okay thanks alot!

kropot72 · Answer

You're welcome :)

bambimonster · Answer

(f)  The United States has ten times the population of Canada.  Assuming equal standard deviations, how many American teenagers must be sampled in order to estimate the true mean amount of time American teenagers spend on the internet per day to within 15 minutes with 95% confidence?

bambimonster · Answer

@kropot72

bambimonster · Answer

i got 23 as answer.. can u help me check

kropot72 · Answer

I agree with your answer. The size of the population does not come into the calculation, however the population standard deviation of daily internet usage time must be known which is the same for both calculations.

bambimonster · Answer

so as long as i round up my answers.. and follow the equation.. i should get the correct answer right? why is that we wud have to round it up even though it is not 5 or above 5(d.p)

kropot72 · Answer

Because if you round down, the sample will not be large enough to estimate the mean within the given limits at the given confidence level.