# 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?

Oct 5, 2015

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

${H}_{o}$: $\sigma \ge 2.5$
${H}_{a}$: $\sigma < 2.5$

STEP 2
State your test statistic, assumptions, conditions and significance level.

Test Statistic : ${\chi}^{2}$ = (n−1)( s²) / (sigma²) with df = n− 1

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:

$\alpha = 0.05$

STEP 3
Calculate the test statistic and the p-value.

${\chi}^{2}$ = (20−1)( 2.0365²) / (2.5²) = 12.61
with df = 20− 1=19

P-value = $P r \left({\chi}^{2} < 12.61\right) = 0.1421$
[Note: I used a TI-84 calculator using 19 d.f.]

STEP 4