Question

• Using the two-sample hypothesis test comparing old call time to new call time at a .05 level of significance, discuss the hypothesis test assumptions and tests used. Provide the test statistic and p-value in your response. Evaluate the results of the hypothesis test with the scenario. Provide recommendations for the vice president.
• Using new call time and coded quality, develop a prediction equation for new call time. Evaluate the model and discuss the coefficient of determination, significance, and use the prediction equation to predict a call time if there is a defect.
• Evaluate whether the new call time meets customer specification. As stated in a previous lesson, customers indicated they did not want a call time longer than 7.5 minutes. Assume a standard deviation of 2 min is acceptable. Is the call center now meeting the customer specifications? If not where is the specification not being met? Explain your answers.

thank you so much!!!!

Old Call Time		New Call Time	Shift	Quality	Coded Quality
6.5		5.2	AM	Y	0
6.5		5.2	AM	Y	0
6.5		5.2	AM	Y	0
6.5		5.2	AM	Y	0
7		5.6	AM	Y	0
7		5.6	AM	Y	0
7		5.6	AM	Y	0
7		5.6	AM	N	1
7		5.6	AM	Y	0
8		6.4	AM	Y	0
8		6.4	AM	Y	0
8.5		6.8	AM	Y	0
8.5		6.8	AM	Y	0
9		7.2	AM	Y	0
9		7.2	AM	Y	0
9		7.2	AM	N	1
9		7.2	AM	N	1
9.5		7.6	AM	N	1
9.5		7.6	AM	Y	0
9.5		7.6	AM	Y	0
10		8	AM	Y	0
10		8	AM	Y	0
10		8	AM	Y	0
10		8	AM	Y	0
10		8	AM	Y	0
10.5		8.4	AM	Y	0
10.5		8.4	AM	Y	0
10.5		8.4	AM	Y	0
10.5		8.4	AM	Y	0
10.5		8.4	AM	Y	0
10.5		8.4	AM	Y	0
10.5		8.4	AM	Y	0
10.5		8.4	AM	Y	0
11.5		9.2	AM	Y	0
11.5		9.2	AM	Y	0
11.5		9.2	AM	Y	0
12		9.6	AM	Y	0
12		9.6	AM	Y	0
12		9.6	AM	N	1
12		9.6	AM	Y	0
12.5		10	AM	Y	0
12.5		10	AM	N	1
13		10.4	AM	Y	0
13		10.4	AM	Y	0
13.5		10.8	AM	Y	0
15.5		12.4	AM	Y	0
16		12.8	AM	Y	0
16.5		13.2	AM	Y	0
17		13.6	AM	Y	0
18		14.4	AM	Y	0
6		4.8	PM	Y	0
9		7.2	PM	N	1
9.5		7.6	PM	N	1
10		8	PM	Y	0
10.5		8.4	PM	Y	0
10.5		8.4	PM	Y	0
11		8.8	PM	Y	0
11		8.8	PM	Y	0
11		8.8	PM	Y	0
11		8.8	PM	Y	0
11.5		9.2	PM	Y	0
11.5		9.2	PM	Y	0
11.5		9.2	PM	Y	0
12		9.6	PM	Y	0
12		9.6	PM	Y	0
12		9.6	PM	Y	0
12		9.6	PM	Y	0
12		9.6	PM	Y	0
12		9.6	PM	Y	0
12		9.6	PM	Y	0
12.5		10	PM	Y	0
12.5		10	PM	Y	0
12.5		10	PM	Y	0
12.5		10	PM	Y	0
13		10.4	PM	N	1
13		10.4	PM	N	1
13.5		10.8	PM	Y	0
13.5		10.8	PM	Y	0
14		11.2	PM	Y	0
14		11.2	PM	Y	0
14		11.2	PM	Y	0
14		11.2	PM	N	1
14		11.2	PM	Y	0
14.5		11.6	PM	Y	0
14.5		11.6	PM	Y	0
14.5		11.6	PM	N	1
15		12	PM	N	1
15		12	PM	Y	0
15.5		12.4	PM	N	1
16		12.8	PM	Y	0
16.5		13.2	PM	Y	0
17		13.6	PM	Y	0
17.5		14	PM	Y	0
18		14.4	PM	Y	0
18		14.4	PM	Y	0
18		14.4	PM	Y	0
18.5		14.8	PM	Y	0
19		15.2	PM	Y	0
19.5		15.6	PM	Y	0
19.5		15.6	PM	Y	0
5.25		4.2	AM	Y	0
5.25		4.2	PM	Y	0
5.25		4.2	AM	Y	0
5.25		4.2	PM	Y	0
5.75		4.6	AM	Y	0
5.75		4.6	PM	Y	0
5.75		4.6	AM	Y	0
5.75		4.6	PM	Y	0
5.75		4.6	AM	Y	0
6.75		5.4	PM	Y	0
6.75		5.4	AM	Y	0
7.25		5.8	PM	Y	0
7.25		5.8	AM	Y	0
7.75		6.2	PM	Y	0
7.75		6.2	AM	Y	0
7.75		6.2	PM	N	1
7.75		6.2	AM	Y	0
8.25		6.6	PM	Y	0
8.25		6.6	AM	N	1
8.25		6.6	PM	Y	0
8.75		7	AM	Y	0
8.75		7	PM	Y	0
8.75		7	AM	Y	0
8.75		7	PM	Y	0
8.75		7	AM	Y	0
9.25		7.4	PM	Y	0
9.25		7.4	AM	Y	0
9.25		7.4	PM	Y	0
9.25		7.4	AM	Y	0
9.25		7.4	PM	Y	0
9.25		7.4	AM	Y	0
9.25		7.4	PM	Y	0
9.25		7.4	AM	Y	0
10.25		8.2	PM	Y	0
10.25		8.2	AM	Y	0
10.25		8.2	PM	Y	0
10.75		8.6	AM	Y	0
10.75		8.6	PM	Y	0
10.75		8.6	AM	Y	0
10.75		8.6	PM	Y	0
11.25		9	AM	Y	0
11.25		9	PM	Y	0
11.75		9.4	AM	Y	0
11.75		9.4	PM	Y	0
12.25		9.8	AM	Y	0
14.25		11.4	PM	Y	0
14.75		11.8	AM	Y	0
15.25		12.2	PM	Y	0
15.75		12.6	AM	Y	0
16.75		13.4	PM	Y	0

Answer 1

Using the two-sample hypothesis test comparing old call time to new call time at a .05 level of significance, discuss the hypothesis test assumptions and tests used. Provide the test statistic and p-value in your response. Evaluate the results of the hypothesis test with the scenario. Provide recommendations for the vice president.

We have to use a two-sample hypothesis test comparing old call time to new call time at a .05 level of significance.

The assumptions for the test are:

(i) The sample is normally distributed

(ii) The sample is random and independent

We will perform the two-sample hypothesis test in Excel.

The hypothesis for testing is:

The null hypothesis, H₀: µ₁ = µ₂

The sample average of the old call is the same as the new call.

The alternative hypothesis, H_a: µ₁ ≠ µ₂

The sample average of the old call is not the same as the new call.

Load the data into Excel.

Go to Data>Megastat.

Select the option Hypothesis tests and go to Compare Two Independent Samples.

Select the Group 1 and Group 2 as Old call time and New call time data set respectively.

Click OK.

The output obtained will be as follows:

Old Call Time	New Call Time
11.067	8.853	mean
3.384	2.707	std. dev.
150	150	n
	298	df
	2.2133	difference (Old Call Time - New Call Time)
	9.3885	pooled variance
	3.0641	pooled std. dev.
	0.3538	standard error of difference
	0	hypothesized difference
	6.256	t
	1.37E-09	p-value (two-tailed)

The test statistic, t_stat obtained from the output is 6.256 and p-value is 0.0000.

Since the p-value (0.0000) is less than the significance level(0.05), we can reject the null hypothesis.

Therefore, we have sufficient evidence to conclude that the sample average of the old call is not the same as the new call.

Thus, from the above result, we can recommend to the vice president that the new call time has a better impact and it is wise to maintain the system according to the new call time.

Using new call time and coded quality, develop a prediction equation for new call time. Evaluate the model and discuss the coefficient of determination, significance, and use the prediction equation to predict a call time if there is a defect.

Load the data into Excel.

Go to Data>Megastat.

Select the option Correlation/Regression and go to Regression.

Select Coded Quality as the independent variable, x.

Select New Call Time as the dependent variable, y.

Click OK.

The output will be as follows:

	r²	0.000	n	150
	r	0.009	k	1
	Std. Error	2.716	Dep. Var.	New Call Time
ANOVA table
Source	SS	df	MS	F	p-value
Regression	0.0920	1	0.0920	0.01	.9112
Residual	1,091.7213	148	7.3765
Total	1,091.8133	149
Regression output					confidence interval
variables	coefficients	std. error	t (df=148)	p-value	95% lower	95% upper
Intercept	8.8448
Coded Quality	0.0802	0.7184	0.112	.9112	-1.3394	1.4998

The prediction equation for new call time is:

y = 8.8448 + 0.0808*x

Or

New Call Time = 8.8448 + 0.0808*Coded Quality

The coefficient of determination from the regression output, r²is 0.000.

Since the p-value for overall regression(0.9112) is greater than a reasonable significance level, we cannot reject the null hypothesis and conclude that the model is not significant.

Since the p-value for coefficient Coded Quality(0.9112) is greater than a reasonable significance level, we cannot reject the null hypothesis and conclude that the coefficient is not significant.

When there is a presence of a defect, then the value of Coded Quality will be equal to x =1 and the predicted value of the new call is:

y = 8.8448 + 0.0808*x

y = 8.8448 + 0.0808*1

y = 8.925

Evaluate whether the new call time meets customer specification. As stated in a previous lesson, customers indicated they did not want a call time longer than 7.5 minutes. Assume a standard deviation of 2 min is acceptable. Is the call center now meeting the customer specifications? If not where is the specification not being met? Explain your answers.

In order to test customer satisfaction when the average call duration is 7.5 minutes with a standard deviation of 2 min is acceptable. we want to introduce the Z test for customer satisfaction.

We have:

Sample size, n = 150

The sample mean, y = 8.925

The sample standard deviation, σ = 2

Population mean, µ = 7.5

The hypothesis for testing is:

The null hypothesis, H₀: µ = 7.5

The customer call time is equal to 7.5 minutes.

The alternative hypothesis, H_a: µ₁ < 7.5

The customer call time is less than 7.5 minutes.

Test statistic, z = (y - µ)/σ/√n

= (8.925 - 7.5)/2/√150

= 8.73

The p-value for z = 8.73 is 0.0000.

Since the p-value (0.0000) is less than a reasonable significance level, we can reject the null hypothesis. Thus, we can say that customer call time is less than 7.5 minutes.

Since the new call time is less than 7.5 minutes, the call center is now meeting the customer specifications.