# 95% confidence interval help

#### sinful

##### New Member
How much money does the average professional football fan spend on food at a single football game? That question was posed to ten randomly selected football fans. The sampled result showed that the sample mean and standard deviation were $70.00 and$17.50 respectively. Use this information to create a 95 percent confidence interval for the population mean.

using the zchart I came up with this so far

70+- 1.960(17.50/v-10) (square root of 10)

somehow this is not right, 1.960 should actually be 2.262 and I'm not sure how, any help would be appreciated.

#### JohnM

##### TS Contributor
Because you need to use the t distribution, not the normal distribution. The t statistic for 95% confidence with 9 d.o.f. (10 - 1) is 2.262

#### sinful

##### New Member
hmmm I'm not seeing why to use the t distribution and not normal?

#### JohnM

##### TS Contributor
As a rule of thumb, when the sample size is less than 30 (i.e., "small"), the sampling distribution of the mean more closely follows a t distribution than a normal distribution.

#### sinful

##### New Member
ahhh gotcha, I'm looking the t distribution now and see the 2.262. So the sample size of 10 is what determined to use t distribution? so if the sample size was > than 30 I would have gotten my original answer of 1.960?

#### sinful

##### New Member
also, if my sample size was say 20 which would be (dof 19) it would have been 2.093?

One other question, why would the chart go above 30 if you would use the z if the sample size was greater than 30? Thank you so much for your help btw, I've been trying to figure htis out the past couple hours

#### JohnM

##### TS Contributor
sinful said:
also, if my sample size was say 20 which would be (dof 19) it would have been 2.093?
yes

sinful said:
One other question, why would the chart go above 30 if you would use the z if the sample size was greater than 30? Thank you so much for your help btw, I've been trying to figure htis out the past couple hours
Theoretically, as n increases, the t distribution "approaches" a normal distribution but never really "gets there" exactly. When n>30, we say that it's "close enough."

#### sinful

##### New Member
excellent!! thank you so much for the help! I can now proceed to the next step in studying for my test on Monday..lol