1. The water diet requires one to drink two cups of water every half hour from when one gets up until one goes to bed, but otherwise allows one to eat whatever one likes. Four adult volunteers agree to test the diet. They are weighed prior to beginning the diet and after six weeks on the diet. The weights (in pounds) are

Determine whether there was significant weight loss.

1. State the null and alternative hypothesis for this test.
2. Use the appropriate formula (not a special calculator function or software) to determine the test statistic given by the data
3. What is the P-value of this test? (no calculator)
4. What is your conclusion based on a significance level ofa=0.01? Why?

PERSON	1	2	3	4
Weight before	180	125	240	150
Weight after 6 weeks	170	130	215	152

2. Use a significance level of 0.01 to test the claim that the mean systolic blood pressure of vegetarians is lower than the mean systolic blood pressure of non-vegetarians.

Use the P-value method of hypothesis testing.

vegetarians	Non-vegetarians
N1=85	N2=75
X1=124.1	X2=138.7
S1=38.7	S2=39.2

3. The piston diameter of a certain hand pump is 0.6 inch. the manager determines that the diameters are normally distributed, with a mean of 0.6 inch and a standard deviation of 0.006 inch. after recalibrating the production machine, the manager randomly selects 27 pistons and determines that the standard deviation is 0.0042 inch. Is there significant evidence for the manager to conclude that the standard deviation has decreased at the alpha equals 0.05 level of significance?