Question

The following readings are obtained before and after an internship (showing only the minutes portion of the angle):

Sample 1 (before internship): 24.2 25.2 24.9 24.0 25.2 24.8 24.6 25.1 24.7 24.3

Sample 2 (after internship): 25.1 24.8 24.9 24.5 24.3 25.0 24.5 24.6 24.7

Using an F-test, determine whether the precision of angles measured by the student significantly improved throughout the internship a) at a 90% confidence level b) at a 95% confidence level In other words, test whether the variance of the angles obtained before the internship is significantly larger than that of the angles collected after the internship. Show all necessary steps.

[This includes: • Null hypothesis • Alternative hypothesis • Test statistics • Critical lookup values • State the rejection region • Conclusions o Do not just say whether the null hypothesis was rejected or not rejected. o State what the hypothesis test is telling you Note: Start with computing sample variances for both samples (use n-1 as the denominator).]

Answer 1

BEFORE INTERNSHIP AFTER INTERNSHIP 24.2 25.2 24.9 25.2 24.8 24.6 25.1 24.7 24.3 0.424264069 0.18 25.1 24.8 24.9 24.5 24.3 25 24.5 24.6 24.7 std 0.261937227 variance

NULL HYPOTHESIS H0: $\sigma^2 1= \sigma^2 2$

ALTERNATIVE HYPOTHESIS Ha: $\sigma^2 1> \sigma^2 2$

F= s1^2/s2^2

F= 0.18/0.0686

F= 2.62

F critical values for df1=n1-1= 10-1=9 and df2= n2-1= 9-1=8 at 0.1 level of significance is 2.56

Rejection region: Reject H0 if F cal > F crit =2.56

Since here F cal greater than F crit therefore we reject null hypothesis and conclude that we have sufficient evidence to say that the variance of the angles obtained before the internship is significantly larger than that of the angles collected after the internship.

b) For alpha=0.05

F critical values for df1=n1-1= 10-1=9 and df2= n2-1= 9-1=8 at 0.1 level of significance is 3.388.

Rejection region: Reject H0 if F cal > F crit =3.388

Since here F cal smaller than F crit therefore we fail to reject null hypothesis and conclude that we don't have sufficient evidence to say that the variance of the angles obtained before the internship is significantly larger than that of the angles collected after the internship.