In a sample of 100 households, the mean number of hours spent on social networking sites during the month of January was 50 hours. In a much larger study, the standard deviation was determined to be 6 hours. Assume the population standard deviation is the same. What is the 98% confidence interval for the mean hours devoted to social networking in January?

Question

katecc379 · Answer

The 98% confidence interval ranges from 6 to 50 hours.
 The 98% confidence interval ranges from 48.60 to 51.40 hours.
 The 98% confidence interval ranges from 49.40 to 50.60 hours.
 The 98% confidence interval ranges from 50 to 52 hours.

evoker · Answer

I think you would want to find what z-value yields a 98% chance to be between +z and -z.

katecc379 · Answer

i don't understand

evoker · Answer

nevermind doesn't look like that will work.

katecc379 · Answer

so how do i do this

evoker · Answer

doing some research now, my initial thought was to find what z-interval corresponds to 98% and then add and subtract that many copys of the standard deviation, but none of you answers are close to that answer.

evoker · Answer

That would have been 2.33 standard deviations around the mean of 50 or 50+-14

katecc379 · Answer

still not understanding

sila1453 · Answer

did you find the critical value ?

katecc379 · Answer

idk how to do any of this

evoker · Answer

ok I found according to one source you should use the mean +- the t value times the standard deviation divided by the square root of n.

katecc379 · Answer

so what is n

evoker · Answer

$$\bar x \pm \frac{ t*s }{\sqrt(n) }$$

katecc379 · Answer

and what is the t value times

evoker · Answer

n is the 100 people

evoker · Answer

s is the standard deviation

evoker · Answer

and t comes from a table based on the degrees of freedom and confidence interval

katecc379 · Answer

I'm very confused lol

evoker · Answer

Ok does your text have a t-table in it?

evoker · Answer

I looked online and found for 100 df and 98% confidence interval a t value of 2.364

sila1453 · Answer

isn't it 2.327 ? :o

evoker · Answer

well let's see 2.364*6/10  is approx 1.4

evoker · Answer

Which would give the second answer.

katecc379 · Answer

48.6-51.4?

katecc379 · Answer

no t table

evoker · Answer

That is what I would guess

evoker · Answer

Sorry there are a lot of formulas in statistics, the hardest part is finding the appropriate one for the situation.  But that is my best guess.