A weight loss program claims that program participants have a mean weight loss of at least 12 pounds after 1 month. You work for a medical association and are asked to test this claim. A random sample of 30 program participants and their weight losses (in pounds) after 1 month is listed in the table below. Assume the population standard deviation is 3. At α=0.05, do you have enough evidence to reject the program's claim? 5.1 6 6.1 6.4 7.1 7.6 7.9 8.3 8.4 8.5 8.7 9.1 9.3 9.5 9.6 9.9 10.2 10.3 10.6 10.9 10.9 11 11.5 11.8 11.8 12.2 12.7 12.8 13.1 15.8 Find the standardized test statistic. Find the critical value(s). Decide whether to reject or fail to reject the null hypothesis.
Added by Vincent G.
Step 1
1 Population mean (μ) = 12 Population standard deviation (σ) = 3 Sample size (n) = 30 T = (X̄ - μ) / (σ / √n) T = (10.1 - 12) / (3 / √30) T = -1.9 / (3 / √30) T = -1.9 / (3 / 5.48) T = -1.9 / 0.55 T = -3.45 Show more…
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A weight loss program claims that the program participants have a mean weight loss of at least 11 pounds after 1 month. You work for a medical association and are asked to test this claim. A random sample of 30 program participants was selected and it was found that their mean weight loss (in pounds) was 9.8 pounds with a standard deviation of 3.1 pounds. At alpha = 0.05, do you have enough evidence to reject the program's claim? Use the critical value (rejection region) method. Next, find the standardized test statistic. Round to two decimal places (the hundredths place) if necessary.
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