Question

State the hypotheses, state the test statistic, state the P-value, make your decision, and state a conclusion

In a study to determine whether counseling could help people lose weight, a sample of people experienced a group-based behavioral intervention, which involved weekly meetings with a trained interventionist for a period of six months. The following data are the number of pounds lost for 14 people. It is reasonable to assume the population is normally distributed. Can you conclude that the mean weight loss is greater than 10 pounds? Use ? = 0.05.

18.2	17.3	24.8	33.8	3.9	29.7	20
8.5	17.1	31.2	8.8	19.3	13.4	15.1

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 10
Alternative Hypothesis, Ha: μ > 10

Rejection Region
This is right tailed test, for α = 0.05 and df = 13
Critical value of t is 1.771.
Hence reject H0 if t > 1.771

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (18.65 - 10)/(8.8204/sqrt(14))
t = 3.669

P-value Approach
P-value = 0.0014
As P-value < 0.05, reject the null hypothesis.

Conclusion

There is sufficient evidence to conclude that  the mean weight loss is greater than 10 pounds