Final answer:
The hypothesis test in question is a one-sample t-test to see if participants lost at least 12 pounds on the weight loss program. The primary steps include formulating the null and alternative hypotheses, calculating a test statistic, determining the critical value, and making a decision based on the comparison.
Step-by-step explanation:
The hypothesis test being conducted is a one-sample t-test to determine whether the mean weight loss of program participants is at least 12 pounds after one month. The claim that participants lose at least 12 pounds is the alternative hypothesis (Ha), while the null hypothesis (H0) is that the mean weight loss is less than 12 pounds.
Steps for the hypothesis test
- Formulate the hypotheses: H0: μ < 12 (mean weight loss is less than 12 pounds), Ha: μ ≥ 12 (mean weight loss is at least 12 pounds).
- Choose the significance level (α), commonly 0.05 for a 95% confidence level.
- Calculate the test statistic using the sample mean, standard deviation, and the size of the sample (n).
- Determine the degrees of freedom (df = n - 1).
- Consult the t-distribution table to find the critical value for the chosen α level and degrees of freedom.
- Compare the test statistic to the critical value.
- Make a decision: if the test statistic is greater than the critical value, reject the null hypothesis; otherwise, do not reject it.
- Report the findings and provide an explanation.
Example
Using the provided example of weight loss with a standard deviation of three pounds:
- The sample mean (μ) is hypothesized to be at least 12 pounds.
- The standard deviation (σ) is 3 pounds.
- The sample size (n) is 15.
The test statistic would be calculated, and then a decision would be made based on the t-distribution critical values for a sample size of 15-1=14 degrees of freedom.