Question

Aw, nuts! Refer to Exercise 1.

a. Confirm that the expected counts are large enough to use a chi-square distribution to calculate the P-value. What degrees of freedom should you use?

b. Use Table C to find the P-value. Then use your calculator’s χ2 cdf command.

c. What conclusion would you draw about the company’s claimed distribution for its deluxe mixed nuts?

Short answer

Part (a) The $df=3$

Part (b) $P-$value $=0.0858$

Part (c) There isn't enough evidence to refute the claim concerning the probability distribution in question.

Step-by-step solution

Part (a) Step 1: Given information

Type of count	Count	Frequency	Expected
Cashew	83	52%	78
Almond	29	27%	40.5
Macadamia	20	13%	19.5
Brazil	18	8%	12
Total	150	100%	150

Chi square test statistic$=6.60$

Part (a) Step 2: Calculation

The projected counts are large enough to use a chi-square distribution if all predicted counts are at least $5$This condition is satisfied.

The degrees of freedom $=df=c-1=4-1=3$

Part (b) Step 1: Given information

The degrees of freedom $=df=3$

Part (b) Step 2: Calculation

The $p-$value using table for $df=3$ is,

$0.05<P<0.10$

The excel formula, $=CHIDIST(6.6,3)$

$P-$value$=0.0858$

Part (c) Step 1: Calculation

Chi square test statistic$=6.60$

The degrees of freedom$=df=c-1=4-1=3$

$P-value=0.0858$

Here, $p-value>0.05$fail to reject $H_0$

There isn't enough evidence to refute the claim concerning the probability distribution in question.