Question

1. A dog food manufacturer wants to know if the proper amount of dog food is being placed in their large 200lb bags of dog food. A sample of 100 bags was selected and has the following results: x bar is 197 lbs and s = 1 lb. Find the critical value and the test statistic. Test at alpha of .01

Ho: µ = 200 lbs

Ha: µ ≠ 200 lbs

CV = 2.575 (two tailed test)

TS = (197-200) / (1 / √100) = -3 / .1 = -30 à R Ho

Answer 1

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

The null and alternative hypotheses are given as below:

H0: µ = 200 versus Ha: µ ≠ 200

This is a two tailed test.

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

µ = 200

Xbar = 197

S = 1

n = 100

df = n – 1 = 99

α = 0.01

Critical value = - 2.6264 and 2.6264

(by using t-table or excel)

t = (Xbar - µ)/[S/sqrt(n)]

t = (197 - 200)/[1/sqrt(100)]

t = -30

P-value = 0.0000

(by using t-table)

P-value < α = 0.01

So, we reject the null hypothesis

There is not sufficient evidence to conclude that the proper amount of dog food is being placed in their large 200lb bags of dog food.