statistics

statsexcel.xlsx

Q1

Claim: mean>22	22
Null hypothesis :mean=22
Alternative hypothesis :mean>22
sample mean	23.3
population standard deviation	3.3
samle size	121
sample standard deviation	0.3
test statistic	4.3333333333
p-value	0.0000073434
conclusion	the p-value is less than the alpha therefore there is sufficient evidence to prove that the true population mean is greater than 22.

Claim: mean<$35	35
Null hypothesis :mean=35
Alternative hypothesis :mean>35
sample mean	32.5
population standard deviation	8.1
samle size	18
sample standard deviation	1.9091883092
test statistic	-1.3094570022
p-value	0.0951897968
conclusion	We fail to reject the null hypothesis since the p-value is greater than 0.05 thus the is not suffcient evidence support the claim that mean<$35

Claim: mean=15.4	15.4
Null hypothesis :mean =15.4
Alternative hypothesis :mean≠15.4
sample mean	14.26
population standard deviation	2.5
samle size	35
sample standard deviation	0.4225771274
test statistic	-2.6977323811
p-value	0.006981354
conclusion	The p-value is less than 0.05 thus we reject the null hypothesis and conclude that the mean is significantly different from 15.4.

Claim: mean fleet reliability<=8000	8000
Null hypothesis :mean lfrrt reliability <=8000
Alternative hypothesis :mean>15.4
sample mean	8210
population standard deviation	625
samle size	64
sample standard deviation	78.125
test statistic	2.688
p-value	0.0035940698
conclusion	the p-value is less than 0.05 hence we reject the null hypothesis. There is sufficient evidence to reject the claim that the mean fleet is at most 8000.

Claim: proportion=0.56	0.56
popultion proportion of success	0.56
proportion of failure	0.44
Null hypothesis :proportion =0.56
Alternative hypothesis :proportion≠0.56
sample propotion	0.525
samle size	200
Standard error	0.0350998575
test statistic	-0.997155044
p-value	0.3186892584
conclusion	The p-value is greater than 0.05 thus we fail to reject the null hypothesis. There is sufficient evidence to conclude that the proportion of female students in math courses is equal to the proportion in Elgin Community college.

Cost($thousands)	Sales ($thousands)	Orders	SUMMARY OUTPUT
52.91	380	4012
71.64	441	3801	Regression Statistics
85.57	510	5303	Multiple R	0.9141210782
63.63	403	4264	R Square	0.8356173456
72.87	459	4300	Adjusted R Square	0.8281454068
68.45	450	4097	Standard Error	5.172505409
52.46	305	3212	Observations	24
70.75	488	4803
82.08	513	5231	ANOVA
74.35	508	4732		df	SS	MS	F	Significance F
70.85	540	4415	Regression	1	2992.0995939665	2992.0995939665	111.8340719763	0.0000000004
54.04	353	2928	Residual	22	588.6058685335	26.7548122061
62.93	377	3974	Total	23	3580.7054625
72.29	321	4424
58.94	407	3962		Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
79.39	493	4582	Intercept	2.9498005915	6.4685861572	0.4560193711	0.6528456514	-10.4652260272	16.3648272103	-10.4652260272	16.3648272103
94.48	529	5582	Orders	0.0155959674	0.0014747732	10.5751629763	0.0000000004	0.0125374749	0.0186544599	0.0125374749	0.0186544599
59.72	442	3455
90.53	627	5073
93.21	595	5733	Regresssion equation	y=0.015596x+2.9498
65.63	412	4364		b1	0.015596
72.9	465	4300		b0	2.949801
68.45	450	4097
52.46	305	3212	The number of orders is significant in the determining the warehouse cost since the p-value from the output is less than 0.05. an increase in the number of orders by 1 is associated with a $0.015596 thousand increase in the cost of the warehouse. The model explains 83.56% of the variations in the warehouse cost.
			Predicting warehouse cost when orders=4500
				cost	73.131801
				A warehouse with 4500 orders is predicted to cost $73.1318 thousand.

Claim: proportion<=0.2	0.2
popultion proportion of success	0.2
proportion of failure	0.8
Null hypothesis :proportion <=0.2
Alternative hypothesis :proportion>0.2
x	135
sample propotion	0.27
samle size	500
Standard error	0.0178885438
test statistic	3.9131189606
p-value	0.0000455558
conclusion	The p-value is less than 0.05 thus there is sufficient evidence to reject the null hypothesis. The data gives sufficient evidence to prove that the propotion of favourable response is significantly greater than 0.2.