Question

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?

Answer 1

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.

`H_o`: `sigma>=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 = `Pr(chi^2 < 12.61) = 0.1421`
[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