Chapter 11.1, Problem 9E

To determine

The provided data is sufficient or not is to be stated.

Answer to Problem 9E

There is not sufficient evidence to reject the claim that the Froot Loop produced by Kellogg's contains an equal proportion of each flavour.

Explanation of Solution

Given:

Color	Orange	Yellow	Purple	Red	Blue	Green
Count	$28$	$21$	$16$	$25$	$14$	$16$

Significance level: $5\%=0.05$

Concept Used:

Null hypothesis: $H_0$

The null hypothesis is rejected when the value of $P$ is less or equal to the significance level.

Calculation:

The $P$ value is used to determine the probability of the test statistics or more value extreme.

In the chi-square distribution table, the $P$ -value observed in the appendix which contains $x^2$ value in the row $df=5$ .

  $0.15<P<0.20$

So, the null hypothesis is not rejected when the value of $P$ is not less or equal to the significance level.

  $P>0.05$ : fail to reject $H_0$ .

Hence,

There are is not enough evidence to reject the company’s claim that Froot Loop produced by the Kellogg’s.

Conclusion:

There is not sufficient evidence to reject the claim that the Froot Loop produced by Kellogg's contains an equal proportion of each flavour.