Question

# The bag of snack cheese puffs claims the weight of the contents is 11 ounces. The...

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.

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.

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