Application Problems--Two Means

1. Herman (1967) found Minnesota Teacher Attitude Inventory scores for a sample of 14 athletes and 28 non-athletes. His findings are summarized below. 
              Athletes                     Non-Athletes
               n-1 = 14                    n-2= 28
               Mean-1 = 116.0              Mean-2= 119.54
               s-1 = 31.11                 s-2 = 32.41
Test the hypothesis of the .01 level that in the populations of athletes and non-athletes sample mu-1 equals mu-2.
2. The seasonal rainfall in a country when observed over 16 years, yielded a mean rainfall of 34.5 inches. Suppose it can be assumed that rainfall during a season is normally distributed with a standard deviation s = 7.5. At the .05 level of significance, is the true rainfall in the country less than 40 inches
3. An engineering student measured the daily dissolved oxygen concentration (mg/1) of two streams. The mean daily concentration of stream 1 when observed over 20 days was found to be Mean X = 4.58 and that of stream 2 when observed over 14 days was found to be Mean Y = 3.68. Suppose it is reasonable to assume that daily concentration is normally distributed for each stream and that the concentration of one stream does not influence that of another. Also, it may be assumed that the standard deviation of the concentration of stream 1 is standard deviation-1 = 0.8 and that for stream 2 is standard deviation-2 = 1.1. At the .05 level of significance, is there a difference in the concentrations of the two streams.
4. A distraught professor asserts that students at the university devote less than 10 hours per week to out-of-class study. A questionnaire is distributed to a sample of 300 students. The results show an average allotment of 5.2 hours per week and the standard deviation s = 4.6 hours. Test the authenticity of the professor's assertion at the .05 level.
5. A psychologist wishes to determine whether the persistence of a child at a learning task is significantly affected by the presence of a parent within the learning environment. Two random samples of 15 members each are selected for participation in a study. The mean duration of effort among the children with at least one parent present is 27.3 minutes. Among the other children, the mean duration of effort is 21.9 minutes, the standard deviations are s-1= 6.4 and s-2= 6.8 minutes, respectively. Test they hypothesis of no difference at the .01 level of significance.


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