Question: A random sample of size 12 from a normal population is given below.
69 74 75 76 78 79 81 83 83 85 86 87
a) Someone claimed that s = 10. Does this data set support the claim? Test at a = 0.05.
b) Test if the population mean is 85 using a = 0.05.
c) Find the p-value of the test
we are given that : random sample of size 13 from a normal population.
Part a) We have test if standard deviation is 10 or not ?
Thus we use following steps:
1) State H0 and Ha
2) Find test statistic:
We use chi squares test statistic to test the variance or standard deviation
Thus test statistic is given by:
which follows chi square distribution with n – 1 degrees of freedom
Where S2 =sample variance. Thus we need to find sample variance S2