Question

In a random sample of 22 adults in the U.S., you find that the mean waste generated per person per day is 4.5 pounds with a standard deviation of 1.2 pounds. At @=0.1, can you support the claim that the mean amount of waste generated by adults in the U.S. is more than 4 pounds per day?

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 = 4 versus H_a: µ > 4

This is an upper tailed test.

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

µ = 4

Xbar = 4.5

S = 1.2

n = 22

df = n – 1 = 21

α = 0.10

Critical value = 1.3232

(by using t-table or excel)

t = (Xbar - µ)/[S/sqrt(n)]

t = (4.5 - 4)/[1.2/sqrt(22)]

t = 1.9543

P-value = 0.0321

(by using t-table)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that the mean amount of waste generated by adults in the U.S. is more than 4 pounds per day.