Description
1. (2 points) The mean response time of a species of pigs to a stimulus is .8 seconds.
Twenty- eight pigs were given 2 oz of alcohol and then tested. If their average
response time was 1.0 seconds with a standard deviation of .3 seconds, can we
conclude that alcohol affects the mean response time? Use the 5 percent level of
significance.
2. (2 points) A producer specifies that the mean lifetime of a certain type of battery
is at least 240 hours. A sample of 18 such batteries yielded the following data.
237, 242, 232, 242, 248, 230, 244, 243, 254, 262, 234, 220, 225, 236, 232, 218, 228, 240.
Assuming that the life of the batteries is approximately normally distributed, do
the data indicate that the specifications are not being met?
3. (2 points) A pharmaceutical house produces a certain drug item whose weight has
a standard deviation of 0.5 milligrams. The company’s research team has proposed
a new method of producing the drug. However, this entails some costs and will be
adopted only if there is strong evidence that the standard deviation of the weight
of the items will drop to below 0.4 milligrams. If a sample of 10 items is produced
and has the following weights, should the new method be adopted?
5.728, 5.731, 5.722, 5.719, 5.727, 5.724, 5.718, 5.726, 5.723, 5.722
4. (2 points) Twenty-five men between the ages of 25 and 30, who were participating
in a well- known heart study carried out in Framingham, Massachusetts, were
randomly selected. Of these, 11 were smokers and 14 were not. The following data
refer to readings of their systolic blood pressure.
Smokers : 124, 134, 136, 125, 133, 127, 135, 131, 133, 125, 118.
Nonsmokers : 130, 122, 128, 129, 118, 122, 116, 127, 135, 120, 122, 120, 115, 123.
Use this data to test the hypothesis that the mean blood pressures of smokers and
nonsmokers are the same.
5. (5 points) A purification process for a chemical involves passing it, in solution,
through a resin on which impurities are adsorbed. A chemical engineer wishing to
test the efficiency of 3 different resins took a chemical solution and broke it into
15 batches. She tested each resin 5 times and then measured the concentration of
impurities after passing through the resins. Her data were as follows: Concentration
of Impurities
Resin I: 0.046, 0.025, 0.014, 0.017, 0.043.
Resin II: 0.038, 0.035, 0.031, 0.022, 0.012.
Resin III: 0.031, 0.042, 0.020, 0.018, 0.039.
Test the hypothesis that there is no difference in the efficiency of the resins.
6. (2 points) An experiment was initiated to study the effect of a newly developed
gasoline detergent on automobile mileage. The following data, representing mileage
per gallon before and after the detergent was added for each of eight cars, resulted.
Car without Additive : 24.2, 30.4, 32.7, 19.8, 25.0, 24.9, 22.2, 21.5
Mileage with Additive: 23.5, 29.6, 32.3, 17.6, 25.3, 25.4, 20.6, 20.7
Test the hypothesis that mileage is not affected by the additive when
(a) the sign test is used.
(b) the Wilcoxon signed test is used.
