# Statistics - Hypothesis testing

• Jul 4th 2007, 01:23 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, 11:25 AM
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, 12:41 PM
kaistylez
srs is a simple random sample, tahnks for the reply
• Jul 4th 2007, 02:33 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.

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

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

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

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

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

$\displaystyle P<\alpha$ so we reject the null hypothesis. Therefore, the alternative hypothesis $\displaystyle H_1$ is true and ommitting the annual credit card fee for customers who charge at least $2,400 in a year WILL increase the amount charged on the bank's credit cards. Problem 4, b We know that the c-confidence interval for the population mean of increase is:$\displaystyle \bar{x} - E < \mu < \bar{x} + E\displaystyle \bar{x} - z_c\frac{s}{\sqrt{n}} < \mu < \bar{x} + z_c\frac{s}{\sqrt{n}}$So substituting the given values gives us:$\displaystyle 332 - \frac{2.575\cdot108}{\sqrt{200}} < \mu < 332 + \frac{2.575\cdot108}{\sqrt{200}}\displaystyle 332 - \frac{278.1}{\sqrt{200}} < \mu < 332 + \frac{278.1}{\sqrt{200}}\displaystyle 332 - 19.66 < \mu < 332 + 19.66\displaystyle 312 < \mu < 352\$

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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.