4 (25 pts). in a clinical trial, a pain medicine is used for a sample of patients. The Excel file "Pain treatment" shows the pain level of each patient before and after the treatment.

Use Excel to do the following:

t-Test: Paired Two Sample for Means
	Before	After
Mean	5.547222222	5.466666667
Variance	1.865420635	2.201714286
Observations	36	36
Pearson Correlation	0.972445543
Hypothesized Mean Difference	0
df	35
t Stat	1.363743579
P(T	0.090677788
t Critical one-tail	1.689572458
P(T	0.181355575
t Critical two-tail	2.030107928

1. For each sample, find (i) sample mean, (ii) sample variance.

Before Pain Meds: sample mean = 5.55, sample variance = 1.865

After Pain Meds: sample mean = 5.47, sample variance = 2.201

1. At the ? = 0.05 level of significance use thep-value approach to determine whether there is evidence of a population mean difference before and after the treatment.

P-value = P(T

1. At the ? = 0.05 level of significance use thecritical value approach to determine whether there is evidence of a population mean difference before and after the treatment.