Need help in excel with right tail??

#1
Faced with rising fax costs, a firm issued a guideline that transmissions of 10 pages or more should be sent by 2-day mail instead. Exceptions are allowed, but they want the average to be 10 or below. The firm examined 35 randomly chosen fax transmissions during the next year, yielding a sample mean of 14.44 with a standard deviation of 4.45 pages.
σ=14.44
sd=4.45
n=35

(a) At the .01 level of significance, is the true mean greater than 10?
z = ( 14.44 - 10 ) / ( 4.45 / √ ( 35 ))
z = 5.902785

The p-value = P( Z > z )
= P( Z > 5.902785 )
= 1.787077e-09
this is what I have so far, am I headed in the right direction....

(b) Use Excel to find the right-tail p-value.
Not sure how to apply this to excel......:p
 

TheEcologist

Global Moderator
#2
Faced with rising fax costs, a firm issued a guideline that transmissions of 10 pages or more should be sent by 2-day mail instead. Exceptions are allowed, but they want the average to be 10 or below. The firm examined 35 randomly chosen fax transmissions during the next year, yielding a sample mean of 14.44 with a standard deviation of 4.45 pages.
σ=14.44
sd=4.45
n=35

(a) At the .01 level of significance, is the true mean greater than 10?
z = ( 14.44 - 10 ) / ( 4.45 / √ ( 35 ))
z = 5.902785

The p-value = P( Z > z )
= P( Z > 5.902785 )
= 1.787077e-09
this is what I have so far, am I headed in the right direction....

(b) Use Excel to find the right-tail p-value.
Not sure how to apply this to excel......:p
You should use:

NORMSDIST(Z-value)
for a z-test

and

TDIST(t-value, df, 1) # the 1 specifies one tailed
for a t-test
 
#5
TheEcologist, I really didnt catch that, could u explain in details, step by step, a little new to this 2007 Excel!

I went to NORMSDIST......

NORMSDIST(Z-value) for a z-test (What should I be entering here)
 

TheEcologist

Global Moderator
#6
TheEcologist, I really didnt catch that, could u explain in details, step by step, a little new to this 2007 Excel!

I went to NORMSDIST......

NORMSDIST(Z-value) for a z-test (What should I be entering here)
I'm using Excel 2003:

You calculate your Z-score just as you did above, only instead of using a table you just fill in that value in Excel. It returns the proportion of smaller values in the population (the p-value).

See this useful post: http://www.talkstats.com/showthread.php?t=4593

Lets say you calculated a z-score of -1.645

NORMSDIST(-1.645) returns P=0.049984906, so about 5 % of values will be smaller.

Lets say you calculated a z-score of 1.645

NORMSDIST(1.645) returns P=0.950015094, so about 95 % of values are smaller. However you're not interested in how many are smaller, you need the right-tailed p-value, the proportion of larger values. Now if you know how many are smaller, you automatically know how many are larger, 5%.

100 - 95 = 5

So

NORMSDIST(your z value) returns left tailed p-values, fractions smaller than z
1 - NORMSDIST(your z value) returns right tailed p-values, fractions larger than z.

Now does this help?

see also http://en.wikipedia.org/wiki/Z-test
 
#7
Yes, thats helps great, so:

example if my z-score was 1.975 =

returns p=.975865 so about .02 % will be smaller

So was the problem correct at the top? Should I be using z- score 5.902785 and get the %
 

TheEcologist

Global Moderator
#8
Yes, thats helps great, so:

example if my z-score was 1.975 =

returns p=.975865 so about .02 % will be smaller

So was the problem correct at the top? Should I be using z- score 5.902785 and get the %
When not exactly, if your z-score was -1.975, about .02 will be smaller.

1.975 is on the right end of the distribution, so a fraction of about 0.98 would smaller. But 1-0.98 = 0.02 would be larger.



NORMSDIST returns the proportion to the left of your z-score (usefull if you want to know the fraction smaller than your score). 1-NORMSDIST returns the proportion to the right of your z-score (usefull when you want to know the fraction greater than).

Is this clearing this up for you?
 
#9
Thats perfect what you are showin me......getting what you are sayin......

It shows in the course book that:

α Test Statistic Two-Tailed Critical Values Decision

.01 z = −1.975 z.005 = ±2.576 Don’t reject H0

so my question is should I be using that or should I be using z = 5.902785

Is my problem correct @ the top??
 

TheEcologist

Global Moderator
#10
Thats perfect what you are showin me......getting what you are sayin......

It shows in the course book that:

α Test Statistic Two-Tailed Critical Values Decision

.01 z = −1.975 z.005 = ±2.576 Don’t reject H0

so my question is should I be using that or should I be using z = 5.902785

Is my problem correct @ the top??
Problem

H0 true mean <= 10
H1 true mean > 10

Therefore you only need to look at the right side (> 10), one tailed.
You would need to use a Two-Tailed test if the problem was to test if the true mean was not equal to 10 (either greater or smaller than 10).