Question

In a test of the Atkins weight loss program, 41 individuals participated in a randomized trial with overweight adults. After 12 months, the mean weight loss was found to be 2.1 Kg, with a standard deviation of 4.8 Kg. (a) What is the best point estimate for the mean weight loss of all overweight adults who follow the Atkins program? (b) Construct a 90% confidence interval for the mean weight loss for all such subjects? (c) Test the hypothesis that the mean weight loss is 3.2 Kg. (d) In part (c), could we conclude the test simply by looking at the confidence interval constructed in part (b)? Explain. Also, what is the minimum mean weight loss that would be rejected by the sample data? (e) Suppose that a weight loss program is considered effective only if the weight loss is at least 3.2 Kg after 12 months. Do you think, the Atkinson program seems to effective at 90% confidence level? (f) For part (e), could we use the confidence interval constructed in part (b)?

Answer 1

Ans:

a)Best point estimate=2.1

b)n=41

As,n>=30,we can use normal distribution.

90% confidence interval for mean weight loss

=2.1+/-1.645*(4.8/sqrt(41))

=2.1+/-1.23

=(0.87, 3.33)

c)Two tailed test

Test statistic:

z=(2.1-3.2)/(4.8/sqrt(41))

z=-1.47

critical z values=+/-1.645

As,test statistic does not fall in rejection region,we fail to reject the null hypothesis.

Yes,we can also conclude same from confidence interval,as 3.2 is included within the interval.

d)hypothised population mean=3.2

Minimum weight loss=3.2-1.645*(4.8/sqrt(41))=1.97

e)Left tailed test

Test statistic

z=-1.47

critical z value=-1.282

As,test statistic,z is less than -1.282,we reject the null hypothesis.

There is sufficient evidence to conclude that program is not effective(i.e. weight loss is less than 3.2)

f)No,as in part b) confidence interval is two sided and we in part e) we need left sided confidence bound.