Question

In: Statistics and Probability

1: Using the two-sample hypothesis test comparing old call time to new call time at a...

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.

2: 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.

3: 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.

Question 3. 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.

Old Data and New Data For This Essay

Old Call Time	New Call Time	Shift	Quality	Coded Quality
6.5	5.2	AM	Y	0	Y= CORRECT
6.5	5.2	AM	Y	0	N=INCORRECT
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

Expert Solution

Steps in a Conducting a Hypothesis Test

Although we listed these at the beginning of the lesson, we reiterate them here for convenience plus we are building on them.

Step 1. Check the conditions necessary to run the selected test and select the hypotheses for that test.:

If Z-test for one proportion: np0?5np0?5 and n(1?p0)?5n(1?p0)?5
If a t-test for one mean: either the data comes from an approximately normal distribution or the sample size is at least 30. If neither, then the data is not heavily skewed and without outliers.

If One Proportion Z-test:

Two-tailed		Right-tailed		Left-tailed
H0:p=p0H0:p=p0	OR	H0:p=p0H0:p=p0	OR	H0:p=p0H0:p=p0
Ha:p?p0Ha:p?p0		Ha:p>p0Ha:p>p0		Ha:p<p0Ha:p<p0

If One Mean t-test

Two-tailed		Right-tailed		Left-tailed
H0:?=?0H0:?=?0	OR	H0:?=?0H0:?=?0	OR	H0:?=?0H0:?=?0
Ha:???0Ha:???0		Ha:?>?0Ha:?>?0		Ha:?<?0Ha:?<?0

Step 2. Decide on the significance level, ??.

Step 3. Compute the value of the test statistic:

If One Proportion Z-test: Z?=^p?p0?p0(1?p0)nZ?=p^?p0p0(1?p0)n

If One Mean t-test: t?=¯x??0S/?nt?=x¯??0S/n

Rejection Region Approach to Hypothesis Testing

Step 4. Find the appropriate critical values for the tests using the Z-table for test of one proportion, or the t-table if a test for one mean. REMEMBER: for the one mean test the degrees for freedom are the sample size minus one (i.e. n - 1). Write down clearly the rejection region for the problem.

One Proportion Z-test	One Mean t-test
Two-Tailed Reject H0H0 if \|Z?\|?Z?/2\|Z?\|?Z?/2	Two-Tailed Reject H0H0 if \|t?\|?t?/2\|t?\|?t?/2
Left-Tailed Reject H0H0 if Z??Z?Z??Z?	Left-Tailed Reject H0H0 if t??t?t??t?
Right-Tailed Reject H0H0 if Z??Z?Z??Z?	Right-Tailed Reject H0H0 if t??t?t??t?

Step 5. Check to see if the value of the test statistic falls in the rejection region. If it does, then reject H0H0 (and conclude HaHa). If it does not fall in the rejection region, do not reject H0H0.

Step 6. State the conclusion in words.

P-value Approach to Hypothesis Testing

Steps 1- Step 3. The first few steps (Step 0 - Step 3) are exactly the same as the rejection region approach.

Step 4. In Step 4, we need to compute the appropriate p-value based on our alternative hypothesis:

If HaHa is right-tailed, then the p-value is the probability the sample data produces a value equal to or greater than the observed test statistic.

If HaHa is left-tailed, then the p-value is the probability the sample data produces a value equal to or less than the observed test statistic.

If HaHa is two-tailed, then the p-value is two times the probability the sample data produces a value equal to or greater than the absolute value of the observed test statistic.

Right-tailed		Left-tailed		Two-tailed
_{P(Z>Z?)P(Z>Z?)}	OR	_{P(Z<Z?)P(Z<Z?)}	OR	_{2×P(Z>\|Z?\|)2×P(Z>\|Z?\|)}
_{\(P(t > t*)}_\) _{at df = n-1}		_{P(t<t?)P(t<t?)} _{at df = n-1}		_{2×P(t>\|t?\|)2×P(t>\|t?\|)} _{at df = n-1}

Step 5. Check to see if the p-value is less than the stated alpha value. If it is, then reject H0H0 (and conclude HaHa). If it is not less than alpha, do not reject H0H0.

orchestra answered 1 year ago

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