Chapter 11, Problem 11PT

To determine

To check: The claim of distributor by conducting a significance test at 5% significance level.

Answer to Problem 11PT

The claim of the distributor is rejected at 5% level of significance.

Explanation of Solution

Given:

The table is:

Regular	261
Premium	51
Supreme	88

Calculation:

The null and alternative hypotheses are:

  $\begin{array}{l}{H}_0:p_1=p_2=p_3\\ H_a:\text{ At least one of }{p}_i\text{ is different}\end{array}$

The calculation for test statistic is done as:

Observed value	Expected value	$\left(O-E\right)$	${\left(O-E\right)}^2$	${\left(O-E\right)}^2/E$
261	240	21	441	1.8375
51	80	-->29	841	10.5125
88	80	8	64	0.8
				${\displaystyle \sum {\left(O-E\right)}^2/E}=13.15$

The test statistc is 13.15

The degree of freedom is calculated as:

  $\begin{array}{c}\text{Degree of freedom =Number of categories - 1}\\ =3-1\\ =2\end{array}$

The p-value using chi-square table at 2 degree of freedom is 0.001395

The p -value is below significance level. The null hypothesis gets rejected. There is enough evidence to not be in favor of the claim of distributor at 5% significance level.