Question

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One of the major measures of the quality of service provided by any organization is the...

One of the major measures of the quality of service provided by any organization is the speed with which it responds to customer complaints. A large family-held department store selling furniture and flooring, including carpet, had undergone a major expansion in the past several years. In particular, the flooring department had expanded from 2 installation crews to an installation supervisor, a measurer, and 15 installation crews. The store had the business objective of improving its response to complaints. The variable of interest was defined as the number of days between when the complaint was made and when it was resolved. Data were collected from 40 complaints that were made in the past year (furniture2.xlsx). (a) The installation supervisor claims that the mean number of days between the receipt of a complaint and the resolution of the complaint is 30 days. To test the claim, build null and alternative hypotheses (for a two-tail test). (b) To conduct a two-tail t test based on the hypotheses in (a), identify the rejection regions (two sides) given the 99% critical level. (c) Using the given data, compute the test statistic for the t test. (d) At the 0.01 level of significance, should the claim be rejected (i.e., the mean number of days is different from 30)? In the critical-value approach, what is your conclusion based on (b) and (c)? Explain. (e) Using the test statistic in (c), determine the p-value for the t test. (f) In the p-value approach, what is your conclusion based on (e)? Explain.

Days
65
43
35
137
31
27
152
22
123
81
74
27
11
19
126
110
110
29
61
35
94
31
26
5
12
4
165
32
29
28
29
26
25
1
14
13
13
10
5
27

Solutions

Expert Solution

(a)

The installation supervisor claims that the Mean number of days between the receipt of a complaint and the resolution of the complaint is 30 days.

Hypothesied Mean : = 30 days

Null hypothesis : Ho :

Alternate Hypothesis : Ha : (Two tailed test)

(b) Two tailed test critical values :

Degrees of freedom = n-1 = 40-1=39

Critical regions , at  

c)

Data were collected from 40 complaints that were made in the past year;

Sample size : n= 40

Sample Data:

x : Days : number of days between the receipt of a complaint and the resolution of the complaint

x: Days
65 17.325 300.1556
43 -4.675 21.85563
35 -12.675 160.6556
137 89.325 7978.956
31 -16.675 278.0556
27 -20.675 427.4556
152 104.325 10883.71
22 -25.675 659.2056
123 75.325 5673.856
81 33.325 1110.556
74 26.325 693.0056
27 -20.675 427.4556
11 -36.675 1345.056
19 -28.675 822.2556
126 78.325 6134.806
110 62.325 3884.406
110 62.325 3884.406
29 -18.675 348.7556
61 13.325 177.5556
35 -12.675 160.6556
94 46.325 2146.006
31 -16.675 278.0556
26 -21.675 469.8056
5 -42.675 1821.156
12 -35.675 1272.706
4 -43.675 1907.506
165 117.325 13765.16
32 -15.675 245.7056
29 -18.675 348.7556
28 -19.675 387.1056
29 -18.675 348.7556
26 -21.675 469.8056
25 -22.675 514.1556
1 -46.675 2178.556
14 -33.675 1134.006
13 -34.675 1202.356
13 -34.675 1202.356
10 -37.675 1419.406
5 -42.675 1821.156
27 -20.675 427.4556
Total 1907 78732.78
Sample mean =1907/40=47.675

Hypothesied Mean : 30
Sample Mean : 47.675
Sample Standard Deviation : s 44.931
Sample Size : n 40
Level of significance : 0.01
Degrees of Freedom : n-1 39

d). Critical regions , at  

As Calculated Value is with in the Critical Values i.e.( -2.7079 < 2.488 < 2.7079 )Fail To Reject Null Hypothesis

Claim : that the Mean number of days between the receipt of a complaint and the resolution of the complaint is 30 days

Should the claim( that the Mean number of days between the receipt of a complaint and the resolution of the complaint is 30 days) be rejected : no

e)

tstat = 2.488 (from c)

p-value for the t-test

As P-Value i.e. is greater than Level of significance i.e (P-value:0.0172 > 0.01:Level of significance); Fail to Reject Null Hypothesis

f)

As P-Value i.e. is greater than Level of significance i.e (P-value:0.0172 > 0.01:Level of significance); Fail to Reject Null Hypothesis

Should the claim( that the Mean number of days between the receipt of a complaint and the resolution of the complaint is 30 days) be rejected : no

-------------------------------------------------------------------------------------------------------------------------------

p-value is ccomputed using excel function

"T.DIST.RT function

Returns the right-tailed Student's t-distribution.

The t-distribution is used in the hypothesis testing of small sample data sets. Use this function in place of a table of critical values for the t-distribution.

Syntax

T.DIST.RT(x,deg_freedom)

The T.DIST.RT function syntax has the following arguments:

• X Required. The numeric value at which to evaluate the distribution.

• Deg_freedom Required. An integer indicating the number of degrees of freedom.


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