Question

I did an “Eggsperiment” with a fellow instructor one day. His calculus class was studying volumes of solids by rotating curves around the x-axis. We first modeled the volume of an egg as an ellipsoid, measured the eggs with calipers, and used the calculus formula. Then, each egg was also measured for volume using a water displacement method. We wanted to know if the two methods agreed or not.

The question we want to answer in this activity: “Is there evidence that the two methods differ?” The data were

The hypotheses for this test are:H0:μd =0

Ha: μd ≠ 0
where μd is the mean of the differences in the volume

measurements obtained from using the two methods.

To run this test, first find the differences between each pair of measurements, enter these differences in the table, and enter these differences in a list in your calculator. Then, run a t-test (#2 on the test menu) on that list of data. (Assume the population is approximately normal.)

a) Find the test-statistic and the P-value.t = P-Value =

b) Based on a significance level of 0.05, what is your conclusion and what does this mean in terms of the problem?

Egg	Calculus	Water Displacement	d
1	60.90	60
2	50.77	58.5
3	49.99	45
4	79.16	75
5	75.91	65
6	54.7	55
7	64.9	62.5
8	62.14	60
9	57.62	60

Answer 1

Solution:

Egg	Calculus	Water Displacement	d
1	60.9	60	0.9
2	50.77	58.5	-7.73
3	49.99	45	4.99
4	79.16	75	4.16
5	75.91	65	10.91
6	54.7	55	-0.3
7	64.9	62.5	2.4
8	62.14	60	2.14
9	57.62	60	-2.38

a) Find the test-statistic and the P-value.

b) Based on a significance level of 0.05, what is your conclusion and what does this mean in terms of the problem?

Since the p-value is greater than 0.05, we, therefore, fail to reject the null hypothesis and there is insufficient evidence to conclude that two methods differ. Hence, we can say that there is no difference between the two methods.