A random sample of 51 observations was selected from a normally distributed population. The sample mean was 88.6, and the sample variance was 38.2. Does the sample show sufficient reason to conclude that the population standard deviation is not equal to 8 at the 0.05 level of significance? Use the p-value method.
#2. A researcher wishes to compare two different groups of students with respect to their mean time to complete a particular task. The time required is determined for each group. The data summary is given below. Test the claim at alpha = 0.05, that there is no difference in variance. Give the critical region, test statistic value, and conclusion for the F test. n1 = 100, s1 = 20 n2=120, s2=34
1. n= 51 ; p_value= 1-α= 1- 0.05 = .95
xa= 88.6 / n = 88.6 / 51 = 1.74
sa= 38.2/ sqrt(n) = 38.2/ 7.14= 5.35
sb = 8
So F = sa²/ sb² = 5.35/8 = 0.67
So since p_value > F , we do not reject the ...
This provides an example of working with significance levels in statistics using p-value and finding critical region, test statistic, and conclusion.