Question

The bag of snack cheese puffs claims the weight of the contents is 11 ounces. The quality control officer tests this with a sample of 8 bags of cheese puffs and finds their weights to be the following 11.8, 8.6,  12.6, 7.9, 6.4, 10.4, 13.6, and 9.1 ounces. Test the claim with a level of significance of 0.01 (assume the population is normally distributed) :

a) write Ho and Ha and identify which is the claim

b) identify whether its left, right or two tailed

c) write the p-value

d) decide whether to reject or fail to reject the null hypothesis

e) interpret the final decision in the context of the original claim.

Answer 1

Solution:

Part a

Here, we have to use one sample t test for the population mean.

The null and alternative hypotheses are given as below:

Null hypothesis: H0: the weight of the contents is 11 ounces.

Alternative hypothesis: Ha: the weight of the contents is not 11 ounces.

H0: µ = 11 versus Ha: µ ≠ 11

Part b

This is a two tailed test.

Part c

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

µ = 11

Xbar = 10.05

S = 2.485385857

n = 8

df = n – 1 = 7

α = 0.01

Critical value = - 3.4995 and 3.4995

(by using t-table or excel)

t = (10.05 – 11)/[ 2.485385857/sqrt(8)]

t = -1.0811

P-value = 0.3155

(by using t-table)

Part d

P-value > α = 0.01

So, we do not reject the null hypothesis

Part e

There is sufficient evidence to conclude that the weight of the contents is 11 ounces.