Question

As part of your work for an environmental awareness​ group, you want to test the claim that the mean waste generated by adults in the country is more than 3 pounds per person per day. In a random sample of 14 adults in the​ country, you find that the mean waste generated per person per day is 3.2 pounds and the standard deviation is 1.9 pounds. At α=0.10​, can you support the​ claim? Assume the population is normally distributed.

​(a) Write the claim mathematically and identify Ho and Ha.

​(b) Find the critical​ value(s) and identify the rejection​ region(s).

​(c) Find the standardized test statistic.

​(d) Decide whether to reject or fail to reject the null hypothesis.

​(e) Interpret the decision in the context of the original claim.

Answer 1

(a)

Claim: The mean waste generated by adults in the country is more than 3 pounds per person per day.

Let µ= Mean waste generated by adults in the country in pounds per person per day.

Thus, Mathematically, the claim is µ > 3

Null Hypothesis: The mean waste generated by adults in the country does not significantly exceed 3 pounds per person per day.

I.e. Ho: µ = 3

Alternate Hypothesis: The mean waste generated by adults in the country significantly exceed 3 pounds per person per day.

i.e. Ha: µ > 3

(b)

We will use a one tailed t test in this case, because in this case we want to test that not only the sample mean would be different significantly from the given value but that it would be in a specific direction—it would be higher. So, it’s a directional or one‐tailed. Also, since the sample size is less than 30, we use t test here.

The significance level, α=0.10​ i.e. the confidence interval is 90%

Using the t table for degree of freedom= 13, α=0.10 (one tailed), t (critical) = 1.35

(c)

Standardized t score, t (calc)= (x- µ)/ σ

Where, x= observed value of the waste generated= 3.2

µ = 3

and σ= 1.9

Thus t (calc)= (3.2- 3)/1.9

= 0.105

(d)

Thus t (calc) < t (critical)

So, we fail to reject the null hypothesis.

(e) Decision: Since we fail to reject the null hypothesis, the mean waste generated by adults in the country is not significantly more than 3 pounds per person per day.