Question

53.7   52.4   73.1   49.6   58.1   54.7   54.7   45.0   74.7   79.4   47.2   52.4   22.3   37.5   76.0   67.3   27.1   84.5   39.9   60.1   27.2   31.1   40.6   44.7   24.1   61.4   43.6   58.9   35.2   58.4 34.0   64.9   55.6   56.5   58.8   41.4   35.6   68.1   34.3   75.5

5. For each of the following values, use the one-tail five percent (5%) criteria and determine if the occurrence of the score would be considered relatively likely or unlikely? (Note: Assume that the researcher is only interested in the extreme low percents of students receiving free or reduced lunch--or the negative end of the normal curve). a. 67.3 b. 84.5 c. 34.0 6. For each of the following scores, use the two-tail five percent (5%) criteria and determine if the occurrence of the score would be considered relatively likely or unlikely? a. 43.6 b. 67.3

Answer 1

i)

mean = 51.49

sd = 16.2066

Z = (X - mean)/sd = (X - 51.49)/16.2066

a)

67.3

z= (67.3 - 51.49)/16.2066

= 0.9755284

critical value for one-tail five percent = 1.645

|z| < 1.645

hence likely

b)

84.5

z = (84.5 - 51.49)/16.2066

= 2.03682

|z | > 1.645

this is unlikely

c)

34

Z =(34 - 51.49)/16.2066

= - 1.07918

|Z| < 1.645

hence likely

ii)

a)

for two-tailed

critical values are 1.96 , -1.96

z = (43.6 - 51.49)/16.2066

= -0.48683

|Z| < 1.96

hence likely

b)

z = (67.3 - 51.49)/16.2066

= 0.97552

z < 1.96

relatively likely