Chapter 11.1, Problem 6E

a.

To determine

To check: If the expected counts are large enough for using the chi-square distribution. Also, compute the degree of freedom

Answer to Problem 6E

The degree of freedom is 2

Explanation of Solution

Given:

Total selected balls are 18, 18 and 2.

Total balls are 200.

The test statistic is 4.0389

Formula used:

The formula to compute the degree of freedom is:

Degree of freedom = Number of categories - 1

The expected counts could be computed as:

  $\begin{array}{l}E\left(\text{Red}\right)=200\times \frac{18}{38}=94.74\\ E\left(Black\right)=200\times \frac{18}{38}=94.74\\ E\left(\text{Green}\right)=200\times \frac{2}{38}=10.53\end{array}$

From above calculations, it is clear that the expected counts are above 5.

The degree of freedom is:

Degree of freedom is 3-1 = 2

b.

To determine

To construct: The figure that shows the p -value

Explanation of Solution

Graph:

The figure showing P -value is constructed as:

  

c.

To determine

To find: The P -value using table and calculator.

Answer to Problem 6E

The P -value is 0.133.

Explanation of Solution

Calculation:

The P -value at 2 degree of freedom using table is:

  $\begin{array}{c}P-value=P\left({\chi }^2>\left|{\chi }_{\text{Statistic}}^2\right|\right)\\ =P\left({\chi }^2>4.039\right)\\ =0.133\end{array}$

Now, the P -value using Ti-83 calculator is:

  

Thus, the P -value is 0.133.

d.

To determine

To draw: The conclusion about the claim of the company

Answer to Problem 6E

There is insufficient evidence to reject the claim of the company.

Explanation of Solution

Calculation:

The P -value is above the significance level. The null hypothesis cannot be rejected. Thus, there is insufficient evidence to reject the claim of the company.