Final answer:
To perform a hypothesis test, calculate the test statistic and find the p-value. The null hypothesis is rejected if the p-value is less than the significance level. In this case, the null hypothesis is rejected, indicating sufficient evidence to support the claim of at least 25 lbs weight loss.
Step-by-step explanation:
In this hypothesis test, we want to test the claim that the average weight loss of patients on a certain weight-loss program in 3 months is at least 25 lbs. The null hypothesis (H0) is that the average weight loss is less than 25 lbs, and the alternative hypothesis (Ha) is that the average weight loss is greater than or equal to 25 lbs.
To perform the test, we calculate the test statistic, which is the sample mean minus the hypothesized mean divided by the sample standard deviation divided by the square root of the sample size. In this case, the test statistic is (19.2 - 25) / (5.4 / sqrt(18)) = -3.333.
Next, we find the p-value, which represents the probability of observing a test statistic as extreme as the one calculated if the null hypothesis is true. The p-value is the area under the tail of the distribution to the right of the test statistic.
Since the p-value is less than the significance level of 10%, we reject the null hypothesis. Therefore, we can conclude that there is sufficient evidence to support the claim that the average weight loss of patients on the weight-loss program in 3 months is at least 25 lbs.