Forty people used a popular weight loss program. The mean weight loss was 3.0 id and the standard deviation was 4.9 lb Use a 0.01 significance level to test the claim that the mean weight loss is greater than 0 lb. Use Table A-3 to find the rangel at values for the P-value
Null hypothesis: μ = 0
Alternative hypothesis: μ > 0
Sample size (n) = 40
Mean weight loss (x̄) = 3.0 lb
Standard deviation (σ) = 4.9 lb
Significance level (α) = 0.01
Calculate the test statistic:
t = (x̄ - μ) / (σ / √n)
t = (3.0 - 0) / (4.9 / √40)
t = 3.0 / (4.9 / √40)
t = 3.0 / (4.9 / 6.32)
t = 3.0 / 0.776
t = 3.86
Degrees of freedom (df) = n - 1 = 40 - 1 = 39
Look up the critical t-value for a one-tailed test with α = 0.01 and df = 39 in Table A-3:
tα = 2.704
Compare the test statistic to the critical t-value:
3.86 > 2.704
Since the test statistic is greater than the critical t-value, we reject the null hypothesis.
Conclusion: There is enough evidence to support the claim that the mean weight loss is greater than 0 lb with a significance level of 0.01.