Question

To investigate an alleged unfair trade practice, the Federal Trade Commission (FTC) takes a random sample of sixteen “5- ounce” candy bars from a large shipment. The mean of the sample weights is 4.85 ounces and the sample standard deviation is 0.1 ounce. It is reasonable to assume the population of candy bar weights is approximately Normally distributed. Based on this sample, does the FTC have grounds to proceed against the manufacturer for the unfair practice of short-weight selling, on average? Answer this question by completing the following steps of a hypothesis test at the 5% significance level.

d. Do you reject or fail to reject the null hypothesis? Why?

e. Does the FTC have grounds to proceed against the manufacturer for the unfair practice of short-weight selling, on average? Explain your answer.

Answer 1

Solution:

d. Do you reject or fail to reject the null hypothesis? Why?

Answer: We reject the null hypothesis. Step by step explanation is given as below:

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

Null hypothesis: H₀: FTC does not have grounds to proceed against the manufacturer for the unfair practice of short-weight selling, on average.

Alternative hypothesis: H_a: FTC has grounds to proceed against the manufacturer for the unfair practice of short-weight selling, on average.

H₀: µ = 5 versus H_a: µ < 5

This is lower tailed or left tailed (one tailed) test.

We are given

Level of significance = α = 0.05 or 5%

Sample mean = Xbar = 4.85

Sample standard deviation = S = 0.1

Sample size = n = 16

Degrees of freedom = df = n – 1 = 16 – 1 = 15

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

t = (4.85 – 5)/[0.1/sqrt(16)]

t = -0.15/[0.1/4]

t = -0.15/0.0250

t = -6.0000

P-value = 0.0000

(by using t-table or excel)

P-value < α = 0.05

So, we reject the null hypothesis

e. Does the FTC have grounds to proceed against the manufacturer for the unfair practice of short-weight selling, on average? Explain your answer.

Yes, FTC has grounds to proceed against the manufacturer for the unfair practice of short-weight selling, on average; because we reject the null hypothesis and conclude the alternative hypothesis.