Question

Using the following data, conduct a hypothesis test (by hand) to see if your sample standard deviation (s) differs significantly from your population standard deviation (σ = 2). Alpha is 0.05 (α = 0.05).

Sample data:

10, 12,10, 9, 11, 10, 11, 9, 11, 10, 9, 10, 11, 10, 8, 9, 11, 10

You will need to:

a) State your alternative hypothesis and null hypothesis

b) Calculate the sample standard deviation (s)

c) Calculate the sample size and degrees of freedom (df)

d) Calculate the test statistic.

e) Find the appropriate critical value using α and df

f) State your final conclusion (i.e. include all three parts)

Answer 1

a)
H0: sigma = 2
Ha: sigma not =2

b)

sample std.dev iation = 0.9984

c)

Sample size = 18 , df = 18-1 = 17

d)

chi^2 = (n-1)s^2/sigma^2
= ((18-1) * 0.9984^2)/2^2
= 4.236

e)

Critical value = (30.1910 , 7.5642)
Decision:

Reject H0 if chi^2 < 30.1910 or chi^2 > 7.5642

f)

Reject H0