Question

As 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 100 patties at random. You calculate that the sample mean weight of patties is 2.6 ounces and the standard deviation of the weight of hamburger patties to be 0.4 ounces.

Required:
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

Kindly check explanation

Explanation:

xbar = 2.6

Sample size, n = 100

s = 0.4

Mean, μ = 4

The test statistic :

(xbar - μ) ÷ s/sqrt(n)

(2.6 - 4) ÷ 0.4/sqrt(25)

1.4 ÷ 0.08

= −17.5

Critical tvalue for 95% confidence interval :

df = n - 1 = 25 - 1 = 24

Tcritical at 0.05/2; df

Tcritical = ±2.064

Since, Tstatistic value does not fall within the Tcritical value ±2.064, we reject the Null

Using the p value from Tstatistic calculator :

P value at t = - 17.5 at 0.05 < 0.000001

Since p value is < 0.05, we reject H0.