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.
Q2
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<$35 Q3 Claim: mean=15.4 15.4 Null hypothesis :mean =15.4 Alternative hypothesis :mean?15.4 sample mean 14.26 population standard deviation 2.5 samle size 35 sample standard deviation 0.4225771274 test statistic -2.6977323811 p-value 0.006981354 conclusion The p-value is less than 0.05 thus we reject the null hypothesis and conclude that the mean is significantly different from 15.4. Q4 Claim: mean fleet reliability<=8000 8000 Null hypothesis :mean lfrrt reliability <=8000 Alternative hypothesis :mean>15.4
sample mean 8210
population standard deviation 625
samle size 64
sample standard deviation 78.125
test statistic 2.688
p-value 0.0035940698
conclusion the p-value is less than 0.05 hence we reject the null hypothesis. There is sufficient evidence to reject the claim that the mean fleet is at most 8000.
Q5
Claim: proportion=0.56 0.56
popultion proportion of success 0.56
proportion of failure 0.44
Null hypothesis :proportion =0.56
Alternative hypothesis :proportion?0.56
sample propotion 0.525
samle size 200
Standard error 0.0350998575
test statistic -0.997155044
p-value 0.3186892584
conclusion The p-value is greater than 0.05 thus we fail to reject the null hypothesis. There is sufficient evidence to conclude that the proportion of female students in math courses is equal to the proportion in Elgin Community college.
Q6
Cost($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.
Q7
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.