At a recent meeting, the manager of a national call center for a major Internet bank made the statement that the average past-due amount for customers who have been called previously about their bills is now no larger than $29.00. Other bank managers at the meeting suggested that this statement may be in error and that it might be worthwhile to conduct a test to see if there is statistical support for the call center manager's statement. The accompanying table contains data for a random sample of 67 customers from the call center population. Assuming that the population standard deviation for past due amounts is known to be $59.00, what should be concluded based on the sample data? Test using α=0.05.
State the appropriate null and alternative hypotheses. Choose the correct answer below.
A. H0: μ < 29.00
HA: μ ≥ 29.00
B. H0: μ ≠ 29.00
HA: μ = 29.00
C. H0: μ ≥ 29.00
HA: μ < 29.00
D. H0: μ > 29.00
HA: μ ≤ 29.00
E. H0: μ = 29.00
HA: μ ≠ 29.00
F. H0: μ ≤ 29.00
HA: μ > 29.00
Calculate the test statistic.
t or z = _____ (Round to two decimal places as needed.)
Find the p-value.
p-value = _____ (Round to three decimal places as needed.)
State the conclusion. Choose the correct answer below.
A. Reject the null hypothesis. There is not sufficient evidence at significance level α=0.05 that the mean past-due amount for customers who have been called is greater than $29.00.
B. Reject the null hypothesis. There is sufficient evidence at significance level α=0.05 that the mean past-due amount for customers who have been called is greater than $29.00.
C. Do not reject the null hypothesis. There is not sufficient evidence at significance level α=0.05 that the mean past-due amount for customers who have been called is not equal to $29.00.
D. Do not reject the null hypothesis. There is sufficient evidence at significance level α=0.05 that the mean past-due amount for customers who have been called is greater than $29.00.
Past Amounts due
82.68
-128.99
75.88
99.71
38.27
40.94
-91.57
95.57
121.87
0.00
0.00
102.87
149.56
54.26
0.00
47.21
78.86
142.01
51.58
218.92
25.86
182.59
1.12
-18.23
2.11
0.00
115.53
0.00
82.58
59.29
57.16
27.11
31.72
-61.46
0.00
52.91
58.12
134.67
40.62
107.24
99.85
184.32
72.03
0.00
151.69
167.47
4.58
65.29
53.53
59.64
313.72
144.94
0.00
0.00
0.00
58.65
68.68
-129.32
76.77
99.57
37.81
40.59
-93.72
95.76
122.72
0.00
0.00