# Statistics - Hypothesis testing

• Jul 4th 2007, 02:23 AM
kaistylez
Statistics - Hypothesis testing
hi, i am having problems currently with these two problems, attached are pictures of the two problems i am having problems with, i dont know what kind of testing i am supposed to use. Also how do i find the p-values? My professor wants me to do these problems in a specific format attached is a rubric on how we should show our work.

http://i42.photobucket.com/albums/e3.../IMG_10221.jpg

here is the first problem

http://i42.photobucket.com/albums/e3.../IMG_10191.jpg

second

http://i42.photobucket.com/albums/e3.../IMG_10211.jpg

thanks in advance for the help
• Jul 4th 2007, 12:25 PM
CaptainBlack
Quote:

Originally Posted by kaistylez

What is SRS, presumably some sort of random sample, but what sort?

Simple Random Sample, Stratified Random Sample, ...?

RonL
• Jul 4th 2007, 01:41 PM
kaistylez
srs is a simple random sample, tahnks for the reply
• Jul 4th 2007, 03:33 PM
rualin
Problem 4, a
This problem is a hypothesis test for the mean of a large sample.

First we identify the null and alternative hypotheses and label the given information.

$H_0: \mu _{increase} \le 0$ Null Hypothesis
$H_1: \mu _{increase} > 0$ Alternative Hypothesis (Claim)

$n=200$
$\bar{x}_{increase}=332$
$s=108$
$\alpha=1\%=0.01$

We assume that the null hypothesis is true and choose to reject it if $P\le\alpha$ and fail to reject it otherwise.

To find the P-value, we first find the z-score of the test statistic and then get the area bounded to its right.

$z_{\bar{x}}=\frac{\bar{x}-\mu}{\sigma_{\bar{x}}} = \frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}$ by the Central Limit Theorem
$=\frac{332-0}{\frac{108}{\sqrt{200}}} \approx \frac{332}{7.34} \approx 43$

Because the alternative hypothesis contains the greater than inequality symbol, the hypothesis test is a right-tailed test and $P\approx 0$.

$P<\alpha$ so we reject the null hypothesis. Therefore, the alternative hypothesis $H_1$ is true and ommitting the annual credit card fee for customers who charge at least \$2,400 in a year WILL increase the amount charged on the bank's credit cards.

Problem 4, b
We know that the c-confidence interval for the population mean of increase is:
$\bar{x} - E < \mu < \bar{x} + E$
$\bar{x} - z_c\frac{s}{\sqrt{n}} < \mu < \bar{x} + z_c\frac{s}{\sqrt{n}}$

So substituting the given values gives us:
$332 - \frac{2.575\cdot108}{\sqrt{200}} < \mu < 332 + \frac{2.575\cdot108}{\sqrt{200}}$
$332 - \frac{278.1}{\sqrt{200}} < \mu < 332 + \frac{278.1}{\sqrt{200}}$
$332 - 19.66 < \mu < 332 + 19.66$
$312 < \mu < 352$

----------

Although it all seems to make sense, the z-score of 43 is ridiculous so I am not completely sure about the correct answer. This is the best I could do... hope it helps.