Question

An airline analyzed whether telephone callers to their reservations office would remain on hold longer if they heard (a) an advertisement from the airline or (b) classical music. For 10 callers randomly assigned to these two conditions, the table shows the data.

Recorded Message	Holding Time Observations
Advertisement	1, 2, 5, 8, 11
Classical Music	7, 8, 9, 13, 15

Question 5:

Choose the correct alternate hypothesis for this test.

a. Ha: The distributions for classical music and advertisements are shifted from each other.

b. Ha: The distribution for classical music is shifted to the left of the distribution for advertisements.

c. Ha: The distribution for classical music is shifted to the right of the distribution for advertisements.

d. Ha: The distributions for classical music and advertisements are the same.

Question 6:

Provide the correct test statistic. Round answer to two decimal places.

Question 7:

Choose the correct p-value.

a. <0.0001

b. 0.0475

c. 0.0029

d. 0.0225

Question 8:

What conclusions can be drawn from this hypothesis test? α = 0.05

a. Fail to reject Ho. Conclude that there is insufficient evidence to claim that the two distributions are not identical.

b. Reject Ho. Conclude that there is sufficient evidence to claim that the distributions are shifted from each other.

c. Reject Ho. Conclude that there is sufficient evidence to claim that the distributions are not identical, and that people wait longer on the phone while listening to airline advertisements rather than classical music.

d. Reject Ho. Conclude that there is sufficient evidence to claim that the distributions are not identical, and that people wait longer on the phone while listening to classical music rather than airline advertisements.

Answer 1

5 -

Assuming that the airline currently uses advertisement and wants to check for the effectiveness of classical music. That is, airlines want to see whether callers wait for long if they play classical music instead of an advertisement.

c. Ha: The distribution for classical music is shifted to the right of the distribution for advertisements.

6 -

Before goin into test statistic lets calculate some descriptive stats for the two samples -

Treatment 1 (Advertisement)

N₁: 5
df₁ = N - 1 = 5 - 1 = 4
M₁: 5.4
SS₁: 69.2
s²₁ = SS₁/(N - 1)

= 69.2/(5-1)

= 17.3


Treatment 2 (Classical music)

N₂: 5
df₂ = N - 1 = 5 - 1 = 4
M₂: 10.4
SS₂: 47.2
s²₂ = SS₂/(N - 1)

= 47.2/(5-1)

= 11.8

Lets calculate the test statistic -

T-value Calculation

s²_p = ((df₁/(df₁ + df₂)) * s²₁) + ((df₂/(df₂ + df₂)) * s²₂)

= ((4/8) * 17.3) + ((4/8) * 11.8)

= 14.55

s²_M1 = s²_p/N₁

= 14.55/5

= 2.91

s²_M2 = s²_p/N₂

= 14.55/5

= 2.91

t = (M₁ - M₂)/√(s²_M1 + s²_M2)

= -5/√5.82

= -2.07

7 -

The p value from the normal distribution table for t values for t value of -2.07 and degrees of freedom 10 - 2 is -

0.036 (For a one tailed hypothesis)

However, this value is not present in the option. This is because, the p value has been taken without considering the degrees of freedom (Which should not e the case, since the sample size is less than 30).

If we do not consider degrees of freedom then the p value will come out to be 0.225.

In both cases conclusion is same, which is mentioned next.

8 -

Since, the p value is less than 0.05, the answer is -

d. Reject Ho. Conclude that there is sufficient evidence to claim that the distributions are not identical, and that people wait longer on the phone while listening to classical music rather than airline advertisements.