# Men ages(20-29) have meanheight 69.3 with s.dev of 2.5 in. An analyst wonders if sd of majorleague players less than 2.5 in. Heights of 20 random players are:72, 74, 71, 72,76,70,77,75,72,72,77,73,75,70,73,74,75,73,74,73. Can you help me find the P value?

##### 1 Answer

Deb - this is an inference test for standard deviation. Use the Chi-square distribution to find the P-value.

#### Explanation:

For any inference test, **always** use the following **4-Step** procedure:

**STEP 1**

*State your hypothesis statement.*

**STEP 2**

*State your test statistic, assumptions, conditions and significance level.*

**Test Statistic** :

Next, check the requirements: is the sample normally distributed and free of outliers. Using my TI-84, I did a box-whisker plot and a quantile plot for normality (not shown) and it appears to be approximately normal with no outliers.

The problem does not state a significance level, so I'll use a common value:

**STEP 3**

*Calculate the test statistic and the p-value.*

with

**P-value =**

[Note: I used a TI-84 calculator using 19 d.f.]

**STEP 4**

*State your conclusion.*

Since the P-value > 0.05, there is no significant evidence that the standard deviation of major league players is less than 2.5%

Hope that helped!

P.S. - here is a helpful website with examples for this type of problem:

http://brownmath.com/stat/stdev1.htm