Question

In: Statistics and Probability

Question 1: Locate the Manufacturer tab. Test to determine if there is a significant difference between...

Question 1:

Locate the Manufacturer tab. Test to determine if there is a significant difference between Mean Value Added by the manufacturer and the mean Cost of Materials in manufacturing assuming a 10% level of significance.

Must complete all the parts to this problem:

PART 1: Use Excel to perform the Test for Equality of Variances. Copy and paste the output from Excel into a word document.
PART 2: Write 1 – 2 sentences on the findings from the Test for Equality of Variances. Which two-sample t-test will be needed (equal variances or unequal variances)? Support your answer by using the output from the Test for Equality of Variances. You must include: the hypotheses for the F-test, a discussion of the p-value, and the decision you reach and why.
PART 3: Run the test you chose in step 2 in Excel (t-test assuming equal variances or unequal variances) to test if there is a significant difference between Mean Value Added by the manufacturer and the mean Cost of Materials in manufacturing assuming a 10% level of significance. Copy and paste the output from Excel into a word document.
PART 4: Write 3 - 4 sentences on the findings from the Two-sample T-test. Is there a significant difference between Mean Value Added by the manufacturer and the mean Cost of Materials in manufacturing assuming a 10% level of significance? Support your answer by using the output from the test. You must include: the hypotheses for the T-test, a discussion of the p-value, and the decision you reach and why.

Data: (Table was too large so I divided each data set into two columns)

Value Added by Mfg.		Cost of Materials
23518	4528	78713	3805
15724	7275	42774	7195
24506	55621	27222	57264
21667	1313	37040	1865
20712	162	12030	163
12640	1907	13674	1682
4258	53	19130	85
35210	747	33521	395
20548	328	19612	255
23442	233	5557	177
287	1717	163	943
1508	6532	314	3527
624	4850	2622	4254
2471	3509	4219	2282
4307	2176	5357	1387
673	2696	1061	1183
817	15739	707	17010
8986	999	10421	565
3145	7838	4140	5432
4076	29180	7125	45696
3806	9061	8994	6913
4276	4200	5504	11184
1239	1410	716	5735
9423	16670	8926	31892
11045	5856	11121	4696
1916	3164	2283	2790
599	3999	364	9364
2063	11750	1813	8720
34	4412	71	3527
1445	27974	1321	31527
10603	6936	12376	4909
5775	19880	9661	21531
10404	7793	19285	6232
13274	3528	18632	1689
1909	21718	2170	19273
4606	10513	7290	12954
5518	9545	8135	11858
12464	18178	12980	23474
5447	22673	4011	14343
2290	19221	5101	16515
4182	23110	3755	18543
2818	41135	2694	60857
2201	17521	3279	21819
18848	25322	20596	13897
9655	6700	10604	5523
15668	14278	24634	12657
25918	9466	28963	12578
30692	13428	8483	11065
17982	3459	6940	7621
17857	38705	8863	29591
9699	84059	2823	44486
38407	13920	29572	13398
3878	105899	3811	223639
3989	45220	1047	42367
4388	7903	2055	7760
4055	2590	1098	4363
16567	1435	11298	1674
25025	9986	34596	8120
59813	3564	27187	5476
31801	21071	19932	8760
8497	29028	9849	18028
28886	31051	46935	16787
12277	2390	11130	1020
11547	14032	13085	8114
26006	415	132880	382
3464	2761	6182	3646
2187	685	4446	506
7079	8327	7091	6604
442	2643	496	1789
	1406		997
	11199		8530

Expert Solution

Test for Equal Variances:

Method

Null hypothesis	All variances are equal
Alternative hypothesis	At least one variance is different
Significance level	α = 0.10

95% Bonferroni Confidence Intervals for Standard Deviations

Sample	N	StDev	CI
Value Added by Mfg.	140	15340.7	(10551.0, 22667.5)
Cost of Materials	140	24569.9	(12944.6, 47394.7)

Individual confidence level = 97.5%

Tests

Method	Test Statistic	P-Value
Multiple comparisons	1.25	0.264
Levene	0.45	0.505

Since the p-value (0.505) is greater than the significance level (0.10), we cannot reject the null hypothesis.

Therefore, we can conclude that all variances are equal.

Two-Sample T-Test and CI:

Method

μ₁: mean of Value Added by Mfg.

µ₂: mean of Cost of Materials

Difference: μ₁ - µ₂

Equal variances are assumed for this analysis.

Descriptive Statistics

Sample	N	Mean	StDev	SE Mean
Value Added by Mfg.	140	12498	15341	1297
Cost of Materials	140	14110	24570	2077

Estimation for Difference

Difference	Pooled StDev	95% CI for Difference
-1612	20482	(-6431, 3207)

Test

Null hypothesis	H₀: μ₁ - µ₂ = 0
Alternative hypothesis	H₁: μ₁ - µ₂ ≠ 0

T-Value	DF	P-Value
-0.66	278	0.511

Since the p-value (0.511) is greater than the significance level (0.10), we cannot reject the null hypothesis.

Therefore, we cannot conclude that there is a significant difference between Mean Value Added by the manufacturer and the mean Cost of Materials in manufacturing.

orchestra answered 2 years ago

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