Question

As a shift manager at a local fast food place, you are responsible for ensuring quality control. You do not want to weigh all the frozen hamburger patties that get delivered by your supplier to make sure they weigh four ounces on average, so you choose 25 patties at random. You calculate that the sample mean weight of patties is 3.4 ounces and the standard deviation of the weight of hamburger patties to be 0.5 ounces.

(a) Test the hypothesis that the population mean weight of patties is equal to 4 ounces.

(b) You are particularly concerned about the population weight being under 4 ounces, is there any reason for concern? Explain using the concept of a confidence interval.

Answer 1

Here we have

mu=4

n=25

Xbar=3.4

sd=0.5

a) Ho: mu =4

Ha: mu=/=4

Since we have sample std deviation only known we have to perform t test

t = (Xbar-mu)/(sd/sqrt(n))

t=(3.4-4)/(0.5/sqrt(25))

t= - 6

Now look for critical t value for 95% conf interval at df=n-1=24

we get t_ck = -2.063899 and +2.063899

While t=-6 doesn't fall under above range we have to reject Ho here

b)For weight under 4 we have to find p value of the test for lower tail

Ho: mu =4

Ha: mu<4

Still t =-6 but the p value becomes 0.000001703654

Since p value of the test is very very less than 0.05 we have to reject Ho and hence we can say that we really need to be concerned about the weight being less than 4 since there is sufficient evidence to prove the alternative hypothesis of weight being less than 4 ounces.

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