in a study of a weight loss program 30 subjects lost a mean of 2.6lbs after 12 months. methods of statistics can be used to show that if this diet had no effect, the likelihood of getting these results is roughly 6 chances in 1000. does the weight loss program have statistical significance? doses the weight loss program have practical significance?

If you are using P ≤ .01, it would be statistically significant. However, averaging 2.6 lbs over a year would not be practically significant. Healthy dieting would average about a pound a week.

To determine if the weight loss program has statistical significance, we need to perform a hypothesis test. In this case, we want to test whether the mean weight loss of 2.6 lbs is significantly different from zero.

The null hypothesis (H0) states that there is no effect from the weight loss program, meaning the mean weight loss is zero. The alternate hypothesis (H1) states that there is a significant effect, meaning the mean weight loss is not zero.

To perform the hypothesis test, we can use a t-test since we are working with sample data and do not know the population standard deviation. We will assume a significance level (α) of 0.05, which is a common choice in hypothesis testing.

The t-test will calculate a p-value, which measures the probability of obtaining a result as extreme as the observed results (or more extreme), assuming the null hypothesis is true. If the p-value is less than the significance level (0.05), we reject the null hypothesis and conclude that there is statistically significant evidence to support the alternate hypothesis.

Now, let's calculate the t-test using the given information. We know that there are 30 subjects and the mean weight loss is 2.6 lbs. However, we also need the standard deviation of the sample to perform the calculation.

Assuming we have the standard deviation (let's say it's σ), we can calculate the t-value using the formula:

t = (mean - hypothesized mean) / (σ / √n)

Since the hypothesized mean is zero, the formula simplifies to:

t = mean / (σ / √n)

Once we have the t-value, we can use statistical software or a t-distribution table to find the corresponding p-value. If the p-value is less than 0.05, we can conclude that the weight loss program has statistical significance.

Regarding the practical significance, that is a separate consideration that takes into account the magnitude of the effect and its importance in real-world terms. Even if the weight loss program has statistical significance, a mean weight loss of 2.6 lbs may not be practically significant if it does not have a meaningful impact on health or well-being.

To assess practical significance, it is necessary to consider the specific context and goals of the weight loss program, as well as any relevant guidelines or benchmarks. For example, if the program's goal is to help individuals achieve a healthy weight and 2.6 lbs is considered a substantial improvement, then the weight loss program may have practical significance. However, if 2.6 lbs falls below the recommended weight loss targets for a given time frame, it may lack practical significance.