SOLUTION: A powder diet is tested on 49 people, and a liquid diet is tested on 36 different people. Of interest is whether the liquid
diet yields a higher mean weight loss than the powder d
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Question 1085998: A powder diet is tested on 49 people, and a liquid diet is tested on 36 different people. Of interest is whether the liquid
diet yields a higher mean weight loss than the powder diet. The powder diet group had a mean weight loss of 42 pounds
with a standard deviation of 12 pounds. The liquid diet group had a mean weight loss of 45 pounds with a standard deviation
of 14 pounds.
a. H0: _______
b. Ha: _______
c. In words, CLEARLY state what your random variable Xor P′ represents.
d. State the distribution to use for the test.
e. What is the test statistic?
f. What is the p-value? In one or two complete sentences, explain what the p-value means for this problem.
g. Use the previous information to sketch a picture of this situation. CLEARLY, label and scale the horizontal axis and
shade the region(s) corresponding to the p-value
H. Indicate the correct decision (“reject” or “do not reject” the null hypothesis), the reason for it, and write an appropriate
conclusion, using complete sentences.
i. Alpha: _______
ii. Decision: _______
iii. Reason for decision: _______
iv. Conclusion: _______
I. Construct a 95% confidence interval for the true mean or proportion. Include a sketch of the graph of the situation.
Label the point estimate and the lower and upper bounds of the confidence interval.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Ho: mean 1<= mean 2, meaning liquid diet causes less or the same weight loss as powder.
Ha:mean 1>mean 2
alpha=0.05 P{reject Ho|ho true}
2 sample t test where (x1 bar-x2 bar)/SE will give a t-statistic with df=83, 0.95, 1 df lost from each group.
Test statistic for 1 way test is t>1.644. Reject if t >1.644, otherwise fail to reject.
t=(45-42)/SE
SE is sqrt (s1^2/n1 + (s2^2/n2))=sqrt (196/36 + 144/49=sqrt(8.38)=2.895
t=3/2.895=1.036
p-value=0.15. That means if the Ho is true, we would have a 15% chance of finding a result this great or more. Since we require a 5% chance or less, we fail to reject Ho.
CI=1.644*2.895=4.76
One way confidence interval is 4.76 should be < the difference in the means. It is not. If a two way confidence interval is desired, there has to be a two way test, and here the question implies a one way test. A two way test would have the question: "is there a difference between the powder and the liquid?"
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