Question

1) Two professors compare their commute times to work. The first professor takes a random sample of 25 days and finds an average commute time of 13.4 minutes and a standard deviation of 55 seconds. The second professor takes a random sample of 20 days and finds an average commute time of 19.6 minutes and a standard deviation of 40 seconds At the .1 significance level, conduct a full and appropriate hypothesis test for the professors to see if the VARIABILITY in the first professor's commute is higher than that of the 2nd.

a) What are the appropriate null and alternative hypotheses?

A		H0:σ1=σ2H1:σ1>σ2
B		H0:σ1=σ2H1:σ1<σ2
C		H0:σ1=σ2H1:σ1≠σ2
D		H0:μ1=μ2H1:μ1>μ2
E		H0:μ1=μ2H1:μ1<μ2
F		H0:μ1=μ2H1:μ1≠μ2

b) Identify the other values given in the problem:

1) ? = 25

2) ? = 13.4

3) ? = 55

4) ? = 20

5) ? = 19.6

6) ? = 40

7) ? = 1

c) Calculate the value of the test statistic.  Round your response to at least 2 decimal places.

F=  

d) What is the corresponding P-value for the test statistic? Round your response to at least 4 decimal places.

e) Make a decision:

Since α (<, >, =, =/) P, we (reject, accept) the null hypothesis (H0, H1)

f) Help write a summary of the results of this hypothesis test:

(There is, There is not, We do not whether there is)  enough evidence in this sample to conclude the standard deviation in the first professor's (class length, commute time, coffee drinking, grades) is (greater than, less than, different from) the second professor's at the α= (.05, .01, .1) significance level because P=

Answer 1

a) The appropriate null and alternative hypotheses are : H₀:σ₁=σ₂ against H₁:σ₁>σ₂

b) Given

c) The test statistic can be written as

which under H₀ follows a F distribution with (n₁ -1, n₂ -1) df.

We reject H₀ at α significance level if P-value < α

Now,

The value of the test statistic =

The corresponding P-value for the test statistic

Since P-value < 0.10, so we reject H₀ at 0.1 significance level.

Conclusion : There is enough evidence in this sample to conclude the standard deviation in the first professor's commute time is greater than the second professor's at the α = 0.10  significance level