Overview
Reply to 2 peers: Instructions
For this discussion post, we are going to run a hypothesis test based on a claim made by a nutrition company. Read the following:
A new weight loss medication claims that the average person taking their medication will lose at least 10 pounds in 60 days. We created an experiment where we used 20 people who took the medication and weighed them up front, then weighed them again after 60 days. The net loss is computed by taking initial weight – weight after 60 days. The following represent the individuals weight loss:
Person 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Net Loss -2 2 18 7 13 -1 18 5 14 0 4 4 12 3 13 -1 -1 14 11 -1
Discussion Prompts
Answer the following questions in your initial post:
What does a negative value represent in my dataset?
Find the mean and standard deviation of this data set. Use the following calculator to help find descriptive statistics: https://www.calculatorsoup.com/calculators/statist... to an external site.
Test the claim using a hypothesis test at the α = 0.1 level. Write out the hypotheses, compute your T value, and make your conclusion based on your results.
What are some other variables that may have impacted results?
Supporting Resources: https://www.youtube.com/watch?v=DlwOTOydeykLinks to an external site.
https://www.youtube.com/watch?v=DEkPZv5ppHILinks to an external site.
My response: Hypothesis Testing for Weight Loss Medication Efficacy
In order to test the assertion of the nutrition company that their drug is able to achieve significant weight loss of an average of 10 pounds per 60 days, we use one-sample t-test with a significance level of α = 0.05. The null hypothesis (H₀) states that μ ≥ 10 pounds, while the alternative hypothesis (H₁) posits that μ < 10 pounds, representing a left-tailed test.
Calculating the sample statistics from the 20 participants yields a mean weight loss of x̄ = 4.85 pounds with a standard deviation of s = 7.23 pounds. The test statistic is computed as t = (4.85 - 10)/(7.23/√20) = -3.19, with degrees of freedom df=19. The p-value associated with it is around 0.0025, which is a big difference to our level of significance.
Since p < 0.05, we reject the null hypothesis, and find that there is enough evidence to disprove the claim by the company. The drug fails to induce an average weight loss of 10 pounds within 60 days. The large range of individual responses as shown by the standard deviation and negative values meaning that some subjects gain weight also works against the effectiveness of the product advertised. These results emphasize the need to ensure that hypothesis testing is conducted rigorously when assessing clinical interventions (Mishra et al., 2019).
Reference
Mishra, P., Pandey, C. M., Singh, U., Gupta, A., Sahu, C., & Keshri, A. (2019). Descriptive statistics and normality tests for statistical data. Annals of Cardiac Anaesthesia, 22(1), 67-72. https://doi.org/10.4103/aca.ACA_157_18Links to an external site.
Peer #1:In this dataset, a negative value means the person actually gained weight instead of losing it during the 60 days. When I ran the descriptive statistics, the mean weight loss came out to about 7.15 pounds, and the sample standard deviation was around 6.90 pounds. To test the company’s claim that people lose at least 10 pounds, I used a one-sample t-test with α = 0.10. My hypotheses were (H_0: \mu = 10) and (H_a: \mu < 10). After plugging in the numbers, I got a t-value of about –1.85. With 19 degrees of freedom, the critical value for a left-tailed test at this alpha level is –1.328. Since my t-value was more negative than the critical value, I rejected the null hypothesis. This means the data doesn’t really support the company’s claim that the average person loses 10 pounds. There are also other things that could have affected how much weight people lost, like how they ate during the 60 days, how active they were, their stress levels, sleep, metabolism, or even how consistently they took the medication. All of that could have influenced the results.
Supporting Resources: https://www.youtube.com/watch?v=DlwOTOydeykLinks to an external site.
https://youtu.be/46SqMrzQQ2wLinks to an external site.
Peer#2:1. What does a negative value represent in my dataset?
The dataset represents the Net Loss of weight, which is calculated as (Initial Weight) - (Weight after 60 days).
A negative value in the dataset represents a person who gained weight over the 60 days, or a negative net loss.
Net Loss > 0: The person lost weight.
Net Loss < 0: The person gained weight.
Net Loss + 0: The person's weight remained unchanged
2. Find the mean and standard deviation of this data set.
x=132/20=6.6 pounds is the mean
Standard deviation is 8.525 pounds
3. Test the claim using a hypothesis test at the a=0.1 level. Write out the hypothesis, compute your T-value, and draw your conclusion based on your results.
The claim is that "an average person taking their medication will lose at least 10 lbs in 60 days."
Sample Mean: 6.6
Sample Standard Deviation: 8.525
Sample Size: 20
Level of Significance: 0.10
State the Hypothesis:
The claim "at least 10 lbs is the null hypothesis(Ho). The alternative hypothesis (H1) is the complement. Since H1 contains the less-than sign, this will be a left-tailed test.
T-statistic:
T-value is -1.784
The conclusion is at the 0.10 level; there is sufficient statistical evidence to reject the null hypothesis H0 in favor of the alternative hypothesis H1.
4. What are some other variables that may have impacted results?
Other variables include dietary habits and genetics, BMI, stress and sleep, different medications, and health status