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.