Question

Crispy-Snax is a popular brand of potato chip. The company sells a Halloween sized snack bag of chips. These snack bags are intended to contain 24g of potato chips. The company want to verify that the packaging and labelling is correct and that the bags do not contain less than 24g. Company scientists take a sample of 12 bags and find the sample mean to be 23.1g. Assuming that the standard deviation of the bag filling is 0.5g, do a hypothesis test of the company's claim of 24g per bag to a 99% level of significance.

a.What are your null and alternative hypotheses?

b.What is your test statistic? What probability distribution does the test statistic have?

c.What is the critical value of the distribution of this test?

d.What is p-value?

e.What is your decision regarding to Ho?

f.Provide, in words, a conclusion for the company's management.

Answer 1

(a)

Hypotheses are:

Test is left tailed.

(b)

Given information:

Since population standard deviation is known so single sample z test will be used.

The test statistics is

(c)

Test is left tailed so using excel function "=NORMSINV(0.01)" the critical value of z is -2.33. (z-table can also be used).

The rejection region:

If z < -2.33, reject H0

Decsion:

Since test statistics lies in the rejection region so we reject the null hypothesis.

(d)
Using excel function "=NORMSDIST(-6.24)" the p-value of the test is

p-value = 0.0000

Since p-value is less than 0.01 so we reject the null hypothesis.

(e)

Reject H0

(f)

We can conclude that the bags contains less than 24g. Company should concerned about this.