Question

# The standard deviation for a certain professor's commute time is believed to be 45 seconds. The...

The standard deviation for a certain professor's commute time is believed to be 45 seconds. The professor takes a random sample of 25 days. These days have an average commute time of 13.4 minutes and a standard deviation of 53 seconds. Assume the commute times are normally distributed. At the .1 significance level, conduct a full and appropriate hypothesis test for the professor.

a) What are the appropriate null and alternative hypotheses?

 A H0:σ2=13.4   H1:σ2≠13.4 B H0:σ=45H1:σ≠45 C H0:μ=13.4 H1:μ≠13.4 D H0:σ=13.4 H1:σ≠13.4 E H0:σ2=45 H1:σ2≠45 F H0:μ=45H1:μ≠45

b) Identify the other values given in the problem:

1) ? = 25

2) ? = 13.4

3) ? = 53

4) ? = .10

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

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 (accept, reject) 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 professor's, Dr. Wright's) commute time is (different from, less than, greater than) 45 seconds at the α= (.1, .01, .05) significance level because  P= ?.

(a)

Correct option:

B.   H0: = 45. H1: 45.

(b)

(1) n = 25

(2) = 13.4

(3) s = 53

(4) = .10

(c)

Test statistic is given by:

(d)

ndf = 25 - 1 = 24

By Technology, P - value = 0.0981

(e)

Since < P, we accept the null hypothesis H0.

(f)

There is not enough evidence in this sample to conclude the standard deviation in the professor's commute time is different from 45 seconds at the = .1 significancelevel because P= 0.0981.