Question

Jennifer’s manager Dr. Jonathan Steinberg wonders whether Healthy Life members needed more chiropractic help in 2019 than in 2018, on average. Jennifer selected a random sample of those who were treated by chiropractic doctors in both years. Data provided. Please help Jennifer Nguyen to check whether annual expenses and number of visits increased, on average. For both tests use Data Analysis t-Test: Paired Two Sample for Means and 2% significance level. Jennifer Nguyen and her manager know that in both cases differences are normally distributed, so here again there is no need to build histograms.

	Number of visits		Annual expenses
Patient #	2018	2019	2018	2019
1	10	11	$340.00	$374.00
2	15	14	$560.00	$476.00
3	24	25	$816.00	$850.00
4	7	4	$238.00	$136.00
5	11	10	$374.00	$340.00
6	19	22	$646.00	$748.00
7	18	15	$612.00	$510.00
8	4	3	$136.00	$162.00
9	25	24	$850.00	$816.00
10	31	35	$1,054.00	$1,190.00
11	7	7	$298.00	$238.00
12	8	9	$272.00	$366.00
13	17	15	$578.00	$510.00
14	10	12	$340.00	$408.00
15	14	15	$476.00	$510.00
16	22	20	$748.00	$680.00
17	6	5	$204.00	$170.00
18	21	24	$774.00	$816.00
19	15	15	$510.00	$570.00
20	12	12	$408.00	$468.00
21	3	4	$140.00	$120.00
22	11	10	$450.00	$420.00
23	2	0	$90.00	$0.00
24	2	4	$80.00	$160.00
25	7	6	$300.00	$280.00

Answer 1

The hypothesis being tested is:

H₀: µ_d = 0

H_a: µ_d < 0

12.840	mean 2018
12.840	mean 2019
0.000	mean difference (2018 - 2019)
1.871	std. dev.
0.374	std. error
25	n
24	df
0.000	t
.5000	p-value (one-tailed, lower)

The p-value is 0.5000.

Since the p-value (0.5000) is greater than the significance level (0.02), we fail to reject the null hypothesis.

Therefore, we cannot conclude that the number of visits increased, on average.

The hypothesis being tested is:

H₀: µ_d = 0

H_a: µ_d < 0

451.760	mean 2018
452.720	mean 2019
-0.960	mean difference (2018 - 2019)
69.470	std. dev.
13.894	std. error
25	n
24	df
-0.069	t
.4727	p-value (one-tailed, lower)

The p-value is 0.4727.

Since the p-value (0.4727) is greater than the significance level (0.02), we fail to reject the null hypothesis.

Therefore, we cannot conclude that annual expenses increased, on average.