Question 1169148: Data show that men between the ages of 20 and 29 in a general population have a mean height of 69.3 inches, with a standard deviation of 2.4 inches. A baseball analyst wonders whether the standard deviation of heights of major-league baseball players is less than 2.4 inches. The heights (in inches) of 20 randomly selected players are shown in the table.
ho:0 = 2.4
h1: o < 2.4
Need to find x to the second power
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! To find the chi-square test statistic ($χ^2$) in this scenario, we use the following formula:
$χ^2 = \frac{(n-1)s^2}{σ_0^2}$
Where:
* $n$ = sample size
* $s$ = sample standard deviation
* $σ_0$ = population standard deviation (from the null hypothesis)
Here's how to break down the problem and find $χ^2$:
1. **Gather the Information:**
* $n = 20$ (sample size)
* $σ_0 = 2.4$ inches (population standard deviation from the null hypothesis)
* You need to calculate $s$ (sample standard deviation) from the table of player heights.
2. **Calculate the Sample Standard Deviation (s):**
* To do this, you'll need the player height data. You'll calculate the sample mean and then use that to calculate the sample standard deviation.
* If you provide the data, I can calculate this for you.
* The formula for sample standard deviation is:
$s = \sqrt{\frac{\sum(x_i - \bar{x})^2}{n-1}}$
Where:
* $x_i$ = each individual height
* $\bar{x}$ = the sample mean
* $n$ = sample size
3. **Calculate the Chi-Square Test Statistic:**
* Once you have the sample standard deviation ($s$), plug the values into the chi-square formula:
$χ^2 = \frac{(20-1)s^2}{(2.4)^2}$
$χ^2 = \frac{19s^2}{5.76}$
**Important Considerations:**
* **Data Entry:** The most crucial step is to accurately enter the player height data to calculate the sample standard deviation.
* **Hypothesis Test:** Remember that this chi-square value is a test statistic. To make a conclusion about the baseball analyst's claim, you would compare this calculated $χ^2$ value to a critical chi-square value from a chi-square distribution table. You'd use the appropriate degrees of freedom ($n-1 = 19$) and the significance level (alpha) you've chosen for the test.
**In summary:** To give you the exact $χ^2$ value, I need the height data from the table. If you provide that, I can walk you through the calculations.
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