For all "hypothesis testing" questions, make sure to provide explicit answers with your work shown for all 11 steps of a hypothesis test.


Diet and Weight Gain

Suppose that 1500 women followed a popular diet for a month. A random sample of 35 of these women was taken and the results for weight gained are shown below.


 n   mean    sd    min    Q1  median     Q3    max
35    6.7   7.3   -2.8   0.7     4.2   10.5   17.2 

Assuming that the standard deviation for all 1500 women was 7.1, test, at the 5% level, that the average weight gain per woman for the month was over 5 pounds.


Cactus Growth

A researcher is investigating the growth of a certain cactus under a variety of environmental conditions. He knows from previous research that the growth of this particular type of cactus is approximately normally distributed with a standard deviation of 1.40 cm. Under the current environmental conditions that he is investigating, however, he does not know the mean. He does hypothesize that it is no more than 4 cm. To test this hypothesis he used a preliminary sample of 10 randomly-selected cacti. He found the sample mean for these cacti to be 3.26 cm. Use this information to test his hypothesis with α=0.05.