Activity in Stating Statistical Hypotheses

For each of the following research problems, state the null hypothesis and the alternative hypothesis.

1. Sample one bottle to see if the beer machine is putting too much beer in the bottle. = 16.02 ounces.

   In this problem we are taking a sample of one observation and seeing how it compares with the population value. We are only interested in the case where the machine is putting too much beer into the bottle so our alternative hypothesis will only involve the greater than case. Our two hypotheses for this problem are:

   
   
2. Is the mean time for running the mile for a group of 20 joggers undergoing a fitness program significantly less than the population value of 10 minutes ()?

   In this research problem we are comparing the mean time for a group of joggers with a known population mean. So our null hypothesis will be

   

   There are three possibilities for the alternative hypothesis.

   1. The joggers mean is less than the population mean.
   2. The joggers mean is greater than the population mean.
   3. The joggers mean is not equal to the population mean, that is to say that it could either by less than or be greater than.

   In this particular case we are concerned with the joggers time being less than the population value so our alternative hypothesis would be:

   
3. Is there a significant difference is tested IQ between a group of students who have taken a special program aimed at changing cognitive functioning as compared with a matched control group who did not participate in the special program?

   In this problem, a very common one in research, we are comparing the means of two groups, an experimental group and a control group. In this case the null hypothesis would be stated as

   

   Again, there are three possibilities for the alternative hypothesis.

   1. The mean of the first group is higher than that of the second group.
   2. The mean of the first group is lower than that of the second group.
   3. The mean of the first group is different than the mean of the second group.

   Since we are interested in the case where there is a signficant difference between the two groups we would select the third option and the alternative hypothesis would be

   
4. Is there a significant correlation between reading and spelling for fifth grade pupils?

   In this research problem we are dealng with the significance of a correlation coefficient. We have a single group of students measured on two variables (reading and spelling). The null hypothesis, the hypothesis of no difference, would be that the correlation is zero. The Greek letter rho is used to represent the population correlation, so the null hypothesis would be

   

   In this problem we are asking if there is a significant correlation between reading and spelling. We did not specify whether we wanted a significant positive correlation or a significant negative correlation. Thus our alternative hypothesis would look for a correlation that was significantly different than zero in either direction or significantly not equal to zero. The alternative hypothesis for this problem would be