Chapter 11.2, Problem 31E

a.

To determine

To explain: The conditions for performing the chi-square test are met.

Explanation of Solution

Given:

Goal	FEMALE	MALE
HSC-HM	14	31
HSC-LM	7	18
LSC-HM	21	5
LSC-LM	25	13

The expected table is,

Goal	FEMALE	MALE
HSC-HM	22.50	15.50
HSC-LM	12.50	12.50
LSC-HM	13	13
LSC-LM	19	22.50

The requirments to use chi-suare test is,

• Two categorical variables.
• Two or more categories for each variable
• Independence of observations
• Expected frequency for each cell are at least 1 or it should be at least 5 for the majority (80%) of the cells.

Since, each condition is satisfied by the given information. Therefore, chi-square test it can be used for the give dataset.

b.

To determine

To compute: The p-value of chi-square test.

Answer to Problem 31E

The p-values is 0.1.621759222E-5.

Explanation of Solution

Given:

From exercise 29, the test statistics is 24.8978.

Formula used:

  $\begin{array}{l}df=\left(n-1\right)\left(m-1\right)\\ p-value=P\left({\chi }^2>{\chi }^2{}_{test}\right)\end{array}$

Calculation:

The degree of freedom for both test values, it can be calculated as

For 27 exercise,

  $\begin{array}{c}df=\left(4-1\right)\left(2-1\right)\\ =3\end{array}$

There is the following commend to find p-value on TI83,

“ ${\chi }^{2}cdf\left(24.8978,99,3\right)$”

The output is,

  

Thus, the p-value is 0.1.621759222E-5.

c.

To determine

To explain: Give an interpretation for the p-value.

Explanation of Solution

From 27, the null and alternative hypothesis,

  $\begin{array}{l}{H}_0:\left(\begin{array}{l}\text{There is no difference in the distribution sports goals }\\ \text{for male and female undergraduates at the university}\end{array}\right)\\ H_1:\left(\begin{array}{l}\text{There is a difference in the distribution sports goals }\\ \text{for male and female undergraduates at the university}\end{array}\right)\end{array}$

If the null hypothesis is true, then p-value is probability of obtaining results as extreme for test statistic value.

If there is no relation between gender and sports goal, then the probability of getting a sample as extreme or more extreme as the given sample is 0.1.621759222E-5.

d.

To determine

To conclude: find the conclusion.

Explanation of Solution

The null hypothesis is rejected when the p-value is less than level of significance.

Here, the p-value is less than level of significance. Thus, the null hypothesis is rejected.

Therefore, there is a sufficient evidence to conclude that there is an association between the variables goal and sex.