Question

A random sample of size 13 from a normal population is given below.

69 74 75 76 78 79 81 83 83 85 86 87 80

a) Someone claimed that sigma = 10. Does this data set support the claim? Test at alpha = 0.05.

b) Test if the population mean is 85 using alpha = 0.05.

c) Find the p-value of the test.

Answer 1

a) n=13
69 74 75 76 78 79 81 83 83 85 86 87 80

sample standard deviation = 5.25

Test statistic:

Chi square = (13-1)*5.25^2/10^2 = 3.31

df = 13-1 = 12

p-value = 0.0142

As,p-value < 0.05, we reject the null hypothesis. There is sufficient evidence to reject the claim.

b) sample mean = 79.69

Test statistic:

t = (79.69-85)/(5.25/sqrt(13)) = -3.65

df=13-1=12

critical t value=tinv(0.05,12)=+/-2.179

As, p-value < 0.05,we reject the null hypothesis.

c) p-value = tdist(3.65,12,2) = 0.0033