Hypothesis testing is a powerful methodology for scientists and analysts alike.

Thankfully, it is a fairly straightforward endeavor, which I’ve outlined below.

Hypothesis Testing - Main Steps
(A)Declare your null hypothesis (Ho)
(B)Declare your alternative hypothesis (Ha)
(C)State your assumptions about your dataset
(D)Set your significance level(alpha α) for your assay
(E)Choose your test and Conduct your experiment
(F)Record observations/results
(G)Compute probability of your results
(H)Make a decision based on your p-value

Here’s a practical example using R:

A new weight loss drug introduced by a British pharmaceutical company claims that, individuals who are clinically diagnosed as obese, will lose 10% of their body weight by taking two pills of this drug a day for 30 days (without changing their lifestyle). Prior to approving this drug for US consumers, FDA wanted to test the potency of the drug. A clinical trial was conducted with a population of 20 obese individuals, treated with this drug for 30 days.

Weightloss.csv

ID	Start Weight	Final Weight
1	321	300
2	300	295
3	350	345
4	360	300
5	400	350
6	250	200
7	281	270
8	278	274
9	330	350
10	374	320
11	280	250
12	421	400
13	245	245
14	352	325
15	312	300
16	279	270
17	233	230
18	310	300
19	265	280
20	275	250

(A)

Null Hypothesis:

Our null hypothesis is that clinically obese patients following the suggested protocol will not lose 10% of their starting weights.

Ho : Weight Lost != 10%

(B)

Alternative Hypothesis:

Our alternative hypothesis is that clinically obese patients following the suggested protocol will lose 10% of their starting weights.

Ha : Weight Lost = 10%

Interpretation Conditions:

Ho : Mu != 10%

Ha : Mu = 10%

(C)

Assumptions

We assumed that our data is continuous, that our group is the result of random sampling, that the participants adhered to the protocols of the study, and that our data is based on a normal distribution.

(D)

Significance

An alpha level of 0.05 was selected for this analysis.

(E)

Test

Our analysis relies on utilizing the T-Statistic, where:

CODE SOLUTION

WeightLoss <- read.csv("https://s3.amazonaws.com/MyData_assets/WeightLoss.csv")

WeightLoss <- startweight - finalweight

samplePercentChange <- WeightLoss/startweight

sampleChangeMean <- mean(percentChange)

tenPercent ← 0.10

sdSamples <- sd(samplePercentChange)

T = ( sampleChangeMean – tenPercent ) / ( sqrt(sdSamples) / sqrt(20) ) = -0.7636174

T-Crit = 2.093

p-value = .454484

p-value > 0.05, not significant

Based on our calculated p-value, we fail to reject our null hypothesis. We can conclude that when following the protocol, and ingesting 2 pills every day for 30 days, clinically obese patients do not achieve a loss of weight equal to 10% of their starting weights under this experimental condition