Question

Use the​ one-standard-deviation chi squared χ2-test and the​ one-standard-deviation

chi squared χ2-interval procedure to conduct the required hypothesis test and obtain the specified confidence interval for a sample of size n=11 with a standard deviation of s=55.

a. Upper H 0H0​:

sigma=66​,

Upper H Subscript aHa​: sigmaσ less than< 6​,

alphα=0.05

b. 90 confidence interval

Answer 1

Ans:

a)

Test statistic:

Chi square=(11-1)*5^2/6^2=6.944

p-value=CHIDIST(6.944,10)=0.2693

As,p-value>0.05,we fail to reject the null hypothesis.There is not sufficient evidence to conclude that standard deviation is less than 6

b)alpha=0.1

alpha/2=0.05

critical chi square values:

CHIINV(0.05,10)=18.307

CHIINV(0.95,10)=3.940

90% confidence interval for population standard deviation:

sqrt(10*5^2/18.307)<sigma<sqrt(10*5^2/3.940)

3.695<sigma<7.965