Critical,Test values

• Mar 29th 2008, 10:06 AM
sweetkendra
Critical,Test values
I am having a bit of a problem with this one. Any help will be appreciated.

A clothing retailer believes that 35% of its customers are between the ages of 20 and 30. A survey of 150 of its customers showed 55 between the ages of 20 and 30. At a 0.10 level of significance, what is the test value? What is the critical value? And Does the data show a contradiction to the retailer's belief?

This is what I have:
p=x/n=55/150=0.366 (0.37) p=0.35 q=1-0.35=0.65
^
z=p-p/sq. rt. pq/n= 0.37-0.35/sq tr. (0.35)(0.65)/150=
• Mar 29th 2008, 11:37 AM
CaptainBlack
Quote:

Originally Posted by sweetkendra
I am having a bit of a problem with this one. Any help will be appreciated.

A clothing retailer believes that 35% of its customers are between the ages of 20 and 30. A survey of 150 of its customers showed 55 between the ages of 20 and 30. At a 0.10 level of significance, what is the test value? What is the critical value? And Does the data show a contradiction to the retailer's belief?

This is what I have:
p=x/n=55/150=0.366 (0.37) p=0.35 q=1-0.35=0.65
^
z=p-p/sq. rt. pq/n= 0.37-0.35/sq tr. (0.35)(0.65)/150=

Well I would work with the numbers rather than the proportions.

Under the null hypothesis (that the retailers belief is true) then the mean
number of customers in the given range out of $150$ is $\mu=52.5$, and the
standard deviation is $\sigma=\sqrt{150 \times 0.35 \times 0.65}$.

Now we will use the normal approximation to the binomial distribution and
assume that the number of such customers is normally distributed with mean
$\mu$ and sd $\sigma$

Now we will reject the null hypothesis if $p(z>z_obs)<0.05$, where

$z_obs=\frac{mu-54.5}{\sigma}$

(that is we have a one sided test.

The critical value for this is: $\approx 1.645$

RonL
• Mar 29th 2008, 12:13 PM
sweetkendra
Critical,Test Values
Thank you for your help CaptainBlack. But can you explain to me how to find the test value?
• Mar 29th 2008, 01:01 PM
CaptainBlack
Quote:

Originally Posted by sweetkendra
Thank you for your help CaptainBlack. But can you explain to me how to find the test value?

You use a table of the cumulative standard normal distribution to do a
reverse table look up - if that makes any sense. Alternativly you need
a peice of technology that will do it for you.

RonL
• Mar 29th 2008, 01:19 PM
sweetkendra
critical, test values
Thank bunches. I have the tables needed.