Question

A call center is concerned that call durations for a customer service representative are too erratic: high variations is call durations can lead to customer dissatisfaction who have to wait longer for a resolution. The company has collected data from 24 randomly selected phone calls from that specific customer representative and found that s = 4.15 minutes. Answer the following questions.

(a) Is there enough evidence to suggest that σ = 4 minutes? Use α = 0.05.

(b) Assume that we do not care about the standard deviation being lower than 4 minutes; instead, we are only interested if the standard deviation is higher than that. Is there enough evidence to suggest that σ = 4 minutes or is it higher than that? Again, you may use that α = 0.05.

Question 2: Testing a variance A call center is concerned that call durations for a customer service representative are too erratic: high variations is call durations can lead to customer dissatisfaction who have to wait longer for a resolution. The company has collected data from 24 randomly selected phone calls from that specific customer representative and found that s = 4.15 minutes. Answer the following questions. (a) Is there enough evidence to suggest that o = 4 minutes? Use a = 0.05. (b) Assume that we do not care about the standard deviation being lower than 4 minutes; instead, we are only interested if the standard deviation is higher than that. Is there enough ev- idence to suggest that o = 4 minutes or is it higher than that? Again, you may use that a = 0.05.

Answer 1

a)
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: σ = 4
Alternative Hypothesis, Ha: σ ≠ 4

Rejection Region
This is two tailed test, for α = 0.05 and df = 24
Critical value of Χ^2 are 12.401 and 39.364
Hence reject H0 if Χ^2 < 12.401 or Χ^2 > 39.364

Test statistic,
Χ^2 = (n-1)*s^2/σ^2
Χ^2 = (25 - 1)*4.15^2/4^2
Χ^2 = 25.834

P-value Approach
P-value = 0.7233
As P-value >= 0.05, fail to reject null hypothesis.

b)
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: σ = 4
Alternative Hypothesis, Ha: σ > 4

Rejection Region
This is right tailed test, for α = 0.05 and df = 24
Critical value of Χ^2 is 36.415
Hence reject H0 if Χ^2 > 36.415

Test statistic,
Χ^2 = (n-1)*s^2/σ^2
Χ^2 = (25 - 1)*4.15^2/4^2
Χ^2 = 25.834

P-value Approach
P-value = 0.3616
As P-value >= 0.05, fail to reject null hypothesis.