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 |
The hypothesis being tested is:
H0: µd = 0
Ha: µd < 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: µd = 0
Ha: µd < 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.
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
Jennifer’s manager Dr. Jonathan Steinberg wonders whether Healthy Life members needed more chiropractic help in 2020 than in 2019, 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 5% significance level. Jennifer Nguyen and her manager know that in both...