Business Statistics (BUS 505) Assignment 10

Hypothesis testing [Page: 342; 1-15]

Answer the question number 01Given that,

16 .4 16 = 15.84 =10%

Our hypothesis is Ho: =16 And, alternative is : < =16

The Decision rule is reject Ho in favor of , if < -

So, < -

= < -1.285

= -1.6 < -1.285 So, our null Hypothesis is rejected.

Answer the question number 02 Given that,

50 3 9 = 48.2 =10%

Our hypothesis is Ho: = = 50 And, alternative is : < = 50 Decision rule is reject Ho in favor of , if

< -

= < -

= -1.8<-1.285According to the decision rule, our significant level for which = -1.285 is bigger than -1.8 .So our null hypothesis is rejected.

Answer the question number 03Given that,

=.03 .004 64 = 3.07 Our hypothesis is Ho: = =.03 And, alternative is : > =.03

Decision rule is reject Ho in favor of , if >

(a) when 5% Significance level ,then

>

=1.4>1.645 According to the decision rule, our significant level for which = 1.645 is bigger so should maintain our null hypothesis.

(b) P-Value: =1.4

Page 1 of 23

Business Statistics (BUS 505) Assignment 10

So, .9192 1- = .9192 =1-.9192 =.0808=8.08%

(c) > or < -

P value is higher because p value two sided so, .0808+.0808= .1616

(d) Here, alternative is more than (>) so we are consider just one side test.

Answer the question number 04 Given that,

3 1.8 100 =2.4

Our hypothesis is Ho: =3 And, alternative is : < =3 Decision rule is reject Null Hypothesis Ho in favor of , if

<- Z=3.33

= -3.33 .9996=1-

=1-.9996 =.0004=.04%

Answer the question number 05 Given that, =4 1.32 1562 =4.27 =1%=.01 .005 Our hypothesis is Ho: = =4 And, alternative is : ≠ =4

Decision rule is reject Null Hypothesis Ho, in favor of , if

> Or, <-

= >

= 8.084 >2.575

According to the decision rule, our significant level /2 for which = 2.575 is not 8.084.So our null hypothesis is rejected.

Answer the question number 06 Given that,

=0 .021 76 =.078 Our hypothesis is Ho: =0 And, alternative is : ≠ P-Value Test: Z=3.38

Z= = =3.38 .9996=1-

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Business Statistics (BUS 505) Assignment 10

=1-.9996 =.0004 2 =.0008=.08%

Answer the question number 07 Given that,

=3.0 .70 172 =3.31 =1% Our hypothesis is Ho: = 3.0

and, alternative is : =3.0Decision rule is reject Null Hypothesis Ho, in favor of , if

= >

= >

=5.808>2.325

So, we reject the null hypothesis.

Answer the question number 08Given that, =0 11.33 170 = - 2.91

Our hypothesis is Ho: = =0 And, alternative is : ≠ =0

Decision rule is reject Null Hypothesis Ho, in favor of , if

Z = <- Z=3.35 .9996=1-

= =1-.9996

=.0004 = - 3.35

Answer the question number 09Given that,

=125.32 25.41 16 =131.78 =5%=.05 .025 Our hypothesis is Ho: = =125.32 And, alternative is : ≠ =125.32

Decision rule is reject Null Hypothesis Ho, in favor of , if

tv = > Or, tv = <-

= >

= 1.02 >2.131

According to the decision rule, Null hypothesis is maintained at level 5%.

Page 3 of 23

Business Statistics (BUS 505) Assignment 10

Answer the question number 11Given that,

=20 10 = =8.82 =5%=.05 .025

Sx= 2.4 Our hypothesis is Ho: = =10 And, alternative is : ≠ =10Decision rule is reject Null Hypothesis Ho, in favor of , if

tv = > Or, tv = <-

= <-

= -1.55 <

According to the decision rule, Null hypothesis is maintained at level 5%.

Answer the question number 12Given that,

=20 9 = =20.35556 =5%=.05 .025

Sx= .612 Our hypothesis is Ho: = =20 And, alternative is : ≠ =20

Decision rule is reject Null Hypothesis Ho, in favor of , if

tv = > Or, tv = <-

= >

= 1.74 >2.306

According to the decision rule, Null hypothesis is maintained at level 5%.

Answer the question number 13Given that,

=78.5 8 =74.5 =10%=.10 .05Sx= 6.2335 Our hypothesis is Ho: = =78.5 And, alternative is : ≠ =78.5

Decision rule is reject Null Hypothesis Ho, in favor of , if

tv = > Or, tv = <-

= <-

= -1.8149<-1.895

Page 4 of 23

Business Statistics (BUS 505) Assignment 10

According to the decision rule, Null hypothesis is maintained at level 10%.

Answer the question number 14Given that, =50 20 =41.3 Sx= 12.2 Our hypothesis is Ho: > =50 And, alternative is : < =50

Decision rule is reject Null Hypothesis Ho, in favor of , if

tv = <-

= <-

= -3.187<-1.729

According to the decision rule, Null hypothesis is rejected at level 5%.

Answer the question number 15Given that, =400 15 =381.35 Sx= 48.60(a) Our hypothesis is Ho: > =400 And, alternative is : < =400Decision rule is reject Null Hypothesis Ho, in favor of , if

tv = <-

= <-

= -1.486<-1.761

According to the decision rule, Null hypothesis is maintained at level 5%. Given that,

=400 50 =381.35 Sx= 48.60

(b) Our hypothesis is Ho: > =400 And, alternative is : < =400

Decision rule is reject Null Hypothesis Ho, in favor of , if

Z = <-Z Z=2.71 F(Z)= .9966

= <- Z 1- =.9966

= -2.71348<- Z = .0034 =.34%

Hypothesis Testing of the Variance[Page: 350; 16-27]

Answer the question number 16

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Business Statistics (BUS 505) Assignment 10

Given that,

So, our null hypothesis is: 500: 20

20 H

And the alternative is:

The decision rule is to reject in favor of if:

At 10% significance level test: so, =

So, 13.076 is bigger than 12.02. According to our decision rule, the null hypothesis is rejected at 10% significant level.

Answer the question number 17 Given that,

a)

b) Given that,

So, our null hypothesis is:

And the alternative is:

The decision rule is to reject in favor of if:

At 5% significance level test: so, =

Therefore, 20.552 is bigger than 16.92. According to our decision rule, the null hypothesis is rejected at 5% significant level.

Answer the question number 18

Given that,

So, our null hypothesis is:

And the alternative is:

The decision rule is to reject in favor of if:

or

Page 6 of 23

[xi = 618, 660, 638, 625, 571, 598, 539, 582]

= 2.641 + 1903.141 + 467.641 + 74.391 + 2058.891 + 337.641 + 511.891 + 1181.641 = 6537.878

[xi =226, 226, 232, 227, 225, 228, 225, 228, 229, 230]

= 2.56 + 2.56 + 19.36 + .36 + 6.76 + .16 + 6.76 + .16 + 1.96 + 5.76 = 46.24

Business Statistics (BUS 505) Assignment 10

At 5% significance level test: so, =

Therefore, according to our decision rule, the null hypothesis is rejected at 5%

Answer the question number 19

Given that,

So, our null hypothesis is:

And the alternative is: =2

The decision rule is to reject in favor of if:

At 5% significance level test: so, =

Therefore, according to our decision rule, the null hypothesis is maintained at 5%

Answer the question number 20

Given that,

So, our null hypothesis is:

And the alternative is:

The decision rule is to reject in favor of if:

At 5% significance level test: so, =

Therefore, 16.96 is not bigger than 13.85. According to our decision rule, the null hypothesis is maintained at 5% significant level.

Answer the question number 21

Given that,

So, our null hypothesis is: And the alternative is: >P0=.25

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Business Statistics (BUS 505) Assignment 10

The decision rule is to reject in favor of if:

=

=2Z=2F(2)=.9772 1- =.9772 =.0228 =2.28%

Answer the question number 22

Given that, n=998 x= (998X17.3%)=173

So, our null hypothesis is: And the alternative is: <P0=.25

The decision rule is to reject in favor of if:

=

=So, we reject that null hypothesis.

Answer the question number 23

Given that, n=160 x= 72

So, our null hypothesis is: And the alternative is: P0=.5The decision rule is to reject in favor of if:

Or

=

=

Z=

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Business Statistics (BUS 505) Assignment 10

F(1.27)=.8980 1- =.8980 =.102 =.204 =20.4%

Answer the question number 24

Given that, n=199 x= 104

So, our null hypothesis is: And the alternative is: P0=.5The decision rule is to reject in favor of if:

Or

Z=

Z=.63799>1.645

So, we are maintained null hypothesis at level 10% level. Z=F(.64)=.7389 1- =.7389 =.2611 =.5222 =52.22%

Answer the question number 25

Given that, n=50 x= 28

So, our null hypothesis is: And the alternative is: >P0=.5The decision rule is to reject in favor of if:

Z=.8485>

Z=.8485F(.85)=.8023 1- =.8023 =.1977 =19.77%

Answer the question number 26

Given that, n=172 x= 118

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Business Statistics (BUS 505) Assignment 10

So, our null hypothesis is: And the alternative is: <P0=.75The decision rule is to reject in favor of if:

Z=

Z=1.94F(1.94)=.9738 1- =.9738 =.0262 =2.62%

Answer the question number 27

Given that, n=202 x= 140

So, our null hypothesis is: And the alternative is: <P0=.75The decision rule is to reject in favor of if:

Z=

Z=1.86F(1.86)=.9686 1- =.9686 =.0314 =3.14%

F-Distribution[Page: 375; 43-47]

Answer the question number 43

Given that,

Our null hypothesis is,

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Business Statistics (BUS 505) Assignment 10

And, alternative hypothesis is,

The decision rule is to reject in favor of if:

At 1% significance level test: so,

Therefore, 3.57 is bigger than 2.477. According to our decision rule, the null hypothesis is rejected at 1% significant level.

Answer the question number 44

Given that,

Our null hypothesis is,

And, alternative hypothesis is,

The decision rule is to reject in favor of if:

At 5% significance level test: so, Therefore, 7.095 is bigger than 4.76. According to our decision rule, the null hypothesis is rejected at 5% significant level.

Answer the question number 45

[From exercise 34] Given that,

Our null hypothesis is,

And, alternative hypothesis is,

The decision rule is to reject in favor of if:

At 2% significance level test: .Now,

= =.439

Therefore, .6922 is not smaller than 439. According to our decision rule, we will maintain the null hypothesis at 2% significant level.

Page 11 of 23

[2.49-1/6(2.49-2.41)= 2.49-.013 = 2.477]

Business Statistics (BUS 505) Assignment 10

Answer the question number 46

[From exercise 36] Given that,

Our null hypothesis is,

And, alternative hypothesis is,

The decision rule is to reject in favor of if:

At 2% significance level test: so, Therefore, 1.571 is not bigger than 5.35. According to our decision rule, we will maintain the null hypothesis at 2% significant level.

Answer the question number 47

[From sxample: 9.8] Given that,

Our null hypothesis is,

And, alternative hypothesis is,

The decision rule is to reject in favor of if:

At 1% significance level test: so, Therefore, 1.459 is not bigger than 29.46. According to our decision rule, we will maintain the null hypothesis at 1% significant level.

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Business Statistics (BUS 505) Assignment 10

Answer the question number 01 [page: 438]X Y XY X2 Y2 Ẏ ( )2 Ẏ- (Ẏ- )2

81 76 6156 6561 5776 81.60 -0.7 0.49 4.9 24.0162 71 4402 3844 5041 68.33 -5.7 32.49 -8.37 70.0674 69 5106 5476 4761 76.71 -7.7 59.29 .01 .000178 76 5928 6084 5776 79.50 -0.7 0.49 2.8 7.8493 87 8091 8649 7569 89.98 10.3 106.09 13.28 176.3669 62 4218 4761 3844 73.22 -14.7 216.09 -3.48 12.1172 80 5760 5184 6400 75.31 3.3 10.89 -1.39 1.9383 75 6225 6889 5625 82.99 -1.7 2.89 6.29 39.5690 92 8280 8100 8464 87.88 15.3 234.09 11.28 124.9984 79 6636 7056 6241 83.69 2.3 5.29 6.99 48.86786 767 60862 62604 59497 799.21 0 668.1 0 505.7245

78.6 76.7

The Correlation is: r =

=

= = =.776

Here r = .776 so we can say that there are some positive relationship.

Hypothesis testing: Here, n=10 r = .776 v=10-2=8

So, our null hypothesis is: And the alternative is: P0=0

We reject H0 if, tv = > tv, or tv = < - tv,

= >

=3.48>2.306

So we can reject null hypothesis at 5% level, and we can accept r = .776.

Linear Regression:Y= a + b x Y=25.03+.6984 X

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Business Statistics (BUS 505) Assignment 10

a = - b = 78.6 - .6984(76.7)=25.03

b = = = =.6984

R2= = =.7569=75.69%

Answer the question number 02 [page: 438]

X Y XY X2 Y2 Ẏ ( )2 Ẏ- (Ẏ- )2

1.5 14.9 22.35 2.25 222.01 9.89 3.08 9.4864 -1.93 3.72.2 -9.2 -1.84 .04 84.64 12.52 -21.02 441.8404 .7 .49-.1 19.6 -1.96 .01 384.16 13.13 7.78 60.5284 1.31 1.71612.8 20.3 56.84 7.84 412.09 7.246 8.48 71.9104 -4.574 20.922.2 -3.7 -8.14 4.84 13.69 8.464 -15.52 240.8704 -3.356 11.26-1.6 27.7 -44.32 2.56 767.29 16.178 15.88 252.1744 4.358 18.99-1.3 22.6 -29.38 1.69 510.76 15.57 10.78 116.2084 3.75 14.065.6 2.3 12.88 31.36 5.29 1.562 -9.52 90.6304 -10.26 105.23-1.4 11.9 -16.66 1.96 141.61 15.77 .08 .0064 3.95 15.601.4 27.0 37.8 1.96 729 10.09 15.18 230.43 -1.73 2.991.5 -4.3 -6.45 2.25 18.49 9.88 -16.12 259.85 -1.94 3.76-4.7 20.3 -95.41 22.09 412.09 22.47 8.48 71.91 10.65 113.421.1 4.2 4.62 1.21 17.64 10.69 -7.62 58.0644 -1.13 1.2777.2 153.6 -69.67 80.06 3718.76 153.46 0 1903.91 0 313.433 .55 11.82

The Correlation is: r =

=

= =.4051

Here r =- .4051 so we can say that there are some nagative relationship.

Hypothesis testing: Here, n=13 r = -.40 v=13-2=11

So, our null hypothesis is: And the alternative is: P0=0

We reject H0 if, tv = > tv, or tv = < - tv,

= < -

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Business Statistics (BUS 505) Assignment 10

=-1.44749 <- 1.796

So we are maintain null hypothesis at 10% level, and we can reject r = -.4051

Linear Regression:Y= a + b x Y=12.93+(-2.02533) X

a = - b = 11.82 - (-2.02533)(.55)=12.93

b = = = =-2.02532

R2= = =.1646=16.46%

Answer the question number 03 [page: 438]

X Y XY X2 Y2 Ẏ ( )2 Ẏ- (Ẏ- )2

2.8 2.6 7.28 7.84 6.76 2.51552 -.35 .1225 -.43448 .188773.7 2.9 10.73 13.69 8.41 2.88793 -.05 .0025 -.06207 .00394.4 3.3 14.52 19.36 10.89 3.17758 .35 .1225 .22758 .051793.6 3.2 11.52 12.96 10.24 2.84655 .25 .0625 -.10345 .010704.7 3.1 14.57 22.09 9.61 3.30172 .15 .0225 .35172 .123703.5 2.8 9.8 12.25 7.84 2.80517 -.15 .0225 -.14483 .020974.1 2.7 11.07 16.81 7.29 3.05345 -.25 .0625 .10345 .010703.2 2.4 7.68 10.24 5.76 2.68104 -.55 .3025 -.26896 .072334.9 3.5 17.15 24.01 12.25 3.38448 .55 .3025 .43448 .188774.2 3.0 12.60 17.64 9 3.09483 -.05 .0025 .14483 .020973.8 3.4 12.92 14.44 11.56 2.92931 .45 .2025 -.03069 .000943.3 2.5 8.25 10.89 6.25 2.72242 -.45 .2025 -.22758 .0517946.2 35.4 138.09 182.22 105.86 35.4 0 1.43 0 .745333.85 2.95

The Correlation is: r =

=

= =.722

Here r =.722 so we can say that there are some positive relationship.

Hypothesis testing: Here, n=12 r = .722 v=12-2=10

So, our null hypothesis is: And the alternative is: > P0=0

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Business Statistics (BUS 505) Assignment 10

We reject H0 if, tv = > tv,

= > = 3.30 > 1.372

So we are reject null hypothesis at 10% level, and we can accept r = .722

Linear Regression:Y= a + b x

Y=1.35691+(.41379) Xa = - b = 2.95 - (.41379)(3.85)=1.35691

b = = = =0.41379

R2= = =.5212=52.12%

Answer the question number 04 [page: 438]

X Y XY X2 Y2 Ẏ ( )2 Ẏ- (Ẏ- )2

7.70 141.77 1091.63 59.29 20098.73 164.775 -18 324 5.005 25.054.17 96.97 404.36 17.39 9403.18 160.00 -62.8 3943.84 .23 .05291.52 163.92 249.16 2.31 26869.77 156.43 4.15 17.22 -3.34 11.156

10.04 154.70 1553.18 100.80 23932.09 167.93 -5.07 25.70 8.16 66.586.02 151.61 912.69 36.24 22985.59 162.51 -8.16 66.59 2.74 7.514.81 147.82 711.01 23.14 21850.75 160.87 -11.95 142.80 1.1 1.211.57 98.61 154.82 2.46 9723.93 156.50 -61.16 3740.55 -3.27 10.693.63 179.18 650.42 13.17 32105.47 159.28 19.41 376.75 -.49 .24011.57 125.19 196.55 2.46 15672.54 156.50 -34.58 1195.78 -3.27 10.69294.65 171.81 798.92 21.62 29518.68 160.66 12.04 144.96 .89 .79212.97 200.23 594.68 8.82 40092.05 158.39 40.46 1637.01 -1.38 1.9044.98 120.49 118.08 .96 14517.84 155.70 -39.28 1542.92 -4.07 16.56494.18 95.83 400.57 17.47 9183.39 160.02 -63.94 4088.32 .25 .06256.09 196.67 1197.72 37.08 38679.09 162.60 36.9 1361.61 2.83 8.00893.09 275.97 852.75 9.55 76159.44 158.55 116.2 13502.44 -1.22 1.48843.08 289.59 891.94 9.49 83862.37 158.54 129.82 16853.23 -1.23 1.51291.76 105.71 186.05 3.09 11174.60 156.76 -54.06 2922.48 -3.01 9.0601

67.83 2716.07 10964.53 365.05 485829.5 2716.02 0 51886.2 0 172.583.99 159.77

The Correlation is: r =

=

= =.05753

Here r =.05753 so we can say that there are some positive relationship.

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Business Statistics (BUS 505) Assignment 10

Hypothesis testing: Here, n=17 r = .05753 v=17-2=15

So, our null hypothesis is: And the alternative is: P0=0

We reject H0 if, tv = > tv, or tv = < - tv,

= >

= .22 >2.131 So we are maintain null hypothesis at 5% level, and we can reject r = .05753

Linear Regression:Y= a + b x

Y=154.38+(1.35) X

a = - b = 159.77 - (1.35)(3.99)=154.38

b = = = =1.35

R2= = =.0033=.3326%

Answer the question number 11

X Y XY X2 Y2 Ẏ ( )2 Ẏ- (Ẏ- )2

2 1 2 4 1 3.68 -11.5 132.25 -8.82 77.794 2 8 16 4 5.36 -10.5 110.25 -7.14 50.981 3 3 1 9 2.84 -9.5 90.25 -9.66 93.3213 4 52 169 16 12.92 -8.5 72.25 .67 .44895 5 25 25 25 6.2 -7.5 56.25 -6.3 39.697 6 42 49 36 7.88 -6.5 42.25 -4.62 21.346 7 42 36 49 7.04 -5.5 30.25 -5.46 29.818 8 64 64 64 8.72 -4.5 20.25 -3.78 14.293 9 27 9 81 4.52 -3.5 12.25 -7.98 63.689 10 90 81 100 9.56 -2.5 6.25 -2.94 8.6417 11 187 289 121 16.28 -1.5 2.25 3.78 14.2919 12 228 361 144 17.96 -.5 .25 5.46 29.81

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Business Statistics (BUS 505) Assignment 10

12 13 156 144 169 12.08 .5 .25 -.42 .1810 14 140 100 196 10.4 1.5 2.25 -2.1 4.4115 15 225 225 225 14.6 2.5 6.25 2.1 4.4118 16 288 324 256 17.12 3.5 12.25 4.62 21.3411 17 187 121 289 11.24 4.5 20.25 -1.26 1.5923 18 414 529 324 21.32 5.5 30.25 8.82 77.7920 19 380 400 361 18.80 6.5 42.25 6.30 39.6916 20 320 256 400 15.44 7.5 56.25 2.94 8.6421 21 441 441 441 19.64 8.5 72.25 7.14 50.9814 22 308 196 484 13.76 9.5 90.25 1.26 1.5922 23 506 484 529 20.48 10.5 110.25 7.98 63.6824 24 576 576 576 22.16 11.5 132.25 9.66 93.32300 300 4711 4900 4900 300 0 1150 0 811.70

12.5 12.5

The Correlation is: r =

=

= =.8357

Here r =.8357 so we can say that there are some positive relationship.

Hypothesis testing: Here, n=24 r = .8357 v=24-2=22

So, our null hypothesis is: And the alternative is: > P0=0

We reject H0 if, tv = > tv,

= >

= 7.137 > 1.717 So we are reject null hypothesis at 5% level, and we can accept r = .8357

Linear Regression:Y= a + b x

Y=2+(.84) X

a = - b = 12.5- (.84) (12.5) =2

b = = = =.84

R2= = =.7058=70.58%

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Business Statistics (BUS 505) Assignment 10

Answer the question number 12

X Y XY X2 Y2 Ẏ ( )2 Ẏ- (Ẏ- )2

1 1 1 1 1 4.03 -9.5 90.25 -6.47 41.862 4 8 4 16 4.71 -6.5 42.25 -5.79 33.523 2 6 9 4 5.39 -8.5 72.25 -5.11 26.114 14 56 16 196 6.07 3.5 12.25 -4.43 19.625 5 25 25 25 6.75 -5.5 30.25 -3.75 14.066 9.5 57 36 90.25 7.43 -1 1 -3.07 9.427 12 84 49 144 8.11 1.5 2.25 -2.39 5.718 7 59.5 72.25 49 9.13 -3.5 12.25 -1.37 1.889 9.5 80.75 72.25 90.25 9.13 -1 1 -1.37 1.8810 11 110 100 121 10.15 .5 .25 -.35 .122511 15 165 121 225 10.83 4.5 20.25 .33 .108912 3 36 144 9 11.51 -7.5 56.25 1.01 1.020113 8 104 169 64 12.19 -2.5 6.25 1.69 2.8614 18 252 196 324 12.87 7.5 56.25 2.37 5.6215 16 240 225 256 13.55 5.5 30.25 3.05 9.3016 13 208 256 169 14.23 2.5 6.25 3.73 13.9117 6 102 289 36 14.91 -4.5 20.25 4.41 19.4518 20 360 324 400 15.59 9.5 90.25 5.09 25.9119 17 323 361 289 16.27 6.5 42.25 5.77 33.2920 19 380 400 361 16.95 8.5 72.25 6.45 41.60210 210 2657.25 2869.5 2869.5 209.8 0 664.5 0 305.3710.5 10.5

The Correlation is: r =

=

= =.6806

Here r =.6806 so we can say that there are some positive relationship.

Hypothesis testing: Here, n=20 r = .6806 v=20-2=18

So, our null hypothesis is: And the alternative is: > P0=0

We reject H0 if, tv = > tv,

= >

= 3.94 > 1.734 So we are reject null hypothesis at 5% level, and we can accept r = .6806

Linear Regression:Y= a + b x

Y=3.35+(.68) X

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Business Statistics (BUS 505) Assignment 10

a = - b = 10.5- (.6806) (10.5) =3.35

b = = = =.6806

R2= = =.4595=45.95%

Answer the question number 13 (Page-455)

X Y XY X2 Y2 Ẏ ( )2 Ẏ- (Ẏ- )2

5.5 420 2310 30.25 176400 410.32 15 225 5.32 28.30276.0 380 2280 36 144400 389.03 -25 625 -15.97 255.04096.5 350 2275 42.25 122500 367.74 -55 3025 -37.26 1388.3086.0 400 2400 36 160000 389.03 -5 25 -15.97 255.04095.0 440 2200 25 193600 431.61 35 1225 26.61 708.09216.5 380 2470 42.25 144400 367.74 -25 625 -37.26 1388.3084.5 450 2025 20.25 202500 452.9 45 2025 47.9 2294.415.0 420 2100 25 176400 431.61 15 225 26.61 708.092145 3240 18060 257 1320200 3239.98 0 8000 0 7025.594

5.625 405

The Correlation is: r =

=

= =-.9371

Here r = - .9371 so we can say that there are some negative relationship.

Hypothesis testing: Here, n=8 r = - .9371 v=8-2=6

So, our null hypothesis is: And the alternative is: P0=0

We reject H0 if, tv = > tv, or tv = < - tv,

= <-

= -6.57 < -2.447 So we are reject null hypothesis at 5% level, and we can accept r = -.9371

Linear Regression:Y= a + b x

Y=644.5125+ (-42.58) X

a = - b = 405 - (-42.58) (5.625) =644.5125

b = = = =-42.58

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Business Statistics (BUS 505) Assignment 10

R2= = =.8782=87.82%

Answer the question number 15 (Page-455)

X Y XY X2 Y2 Ẏ ( )2 Ẏ- (Ẏ- )2

38 4.7 178.6 1444 22.09 5.286 0.276 0.076176 0.862 0.74304424.5 4.7 115.16 600.25 22.09 4.07775 0.276 0.076176 -0.34625 0.11988921.5 4 86 462.25 16 3.80925 -0.424 0.179776 -0.61475 0.37791830.8 4.7 144.76 948.64 22.09 4.6416 0.276 0.076176 0.2176 0.0473520.3 3 60.9 412.09 9 3.70185 -1.424 2.027776 -0.72215 0.52150124 4.4 105.6 576 19.36 4.033 -0.024 0.000576 -0.391 0.152881

29.6 5 148 876.16 25 4.5342 0.576 0.331776 0.1102 0.01214419.4 3.3 64.02 376.36 10.89 3.6213 -1.124 1.263376 -0.8027 0.64432725.6 3.8 97.28 655.36 14.44 4.1762 -0.624 0.389376 -0.2478 0.06140539.5 6.4 252.8 1560.25 40.96 5.42025 1.976 3.904576 0.99625 0.99251423.3 3.3 76.89 542.89 10.89 3.97.035 -1.124 1.263376 -0.45365 0.20579828 3.6 100.8 784 12.96 4.391 -0.824 0.678976 -0.033 0.001089

30.8 4.7 144.76 948.64 22.09 4.6416 0.276 0.076176 0.2176 0.0473532.9 4.4 144.76 1082.41 19.36 4.82955 -0.024 0.000576 0.40555 0.16447130.3 5.4 163.62 918.09 29.36 4.59685 0.976 0.952576 0.17285 0.029877199 3 59.7 396.01 9 3.66605 -1.424 2.027776 -0.75795 0.57448824.6 4.9 120.54 605.16 24.01 4.0867 0.476 0.226576 -0.3373 0.11377132.3 5.2 167.96 1043.29 27.04 4.77585 0.776 0.602176 0.35185 0.12379824.7 4.2 103.74 610.09 17.64 4.09565 -0.224 0.050176 -0.32835 0.10781418.7 3.3 61.71 349.69 10.89 3.55865 -1.124 1.263376 -0.86535 0.74883136.8 4.1 150.88 1354.24 16.81 5.1786 -0.324 0.104976 0.7546 0.56942131.2 6 187.2 973.44 36 4.6774 1.576 2.483776 0.2534 0.06421250.9 5.8 295.22 2590.81 33.64 6.44055 1.376 1.893376 2.01655 4.06647430.7 4.9 150.43 942.49 24.01 4.63265 0.476 0.226576 0.20865 0.04353520.3 3.8 77.14 412.09 14.44 3.70185 -0.624 0.389376 -0.72215 0.521501

708.6 110.6 3258.46 21464.7 509.86 110.5447 0 20.5656 0 11.055428.344 4.424

The Correlation is: r =

=

= =.5420

Here r = .5420 so we can say that there are some positive relationship.

Hypothesis testing: Here, n=25 r = 0.5420 v=25-2=23

So, our null hypothesis is: And the alternative is: P0=0

We reject H0 if, tv = > tv, or tv = < - tv,

= >

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Business Statistics (BUS 505) Assignment 10

= 3.09 > 2.069 So we are reject null hypothesis at 5% level, and we can accept r = 0.5420

Linear Regression:Y= a + b x

Y=1.88757+(0.0895) X

a = - b = 4.424 - (0.0895) (28.34) =1.88757

b = = = =0.0895

R2= = =.5376=53.76%

Answer the question number 18 (Page-455)

X Y XY X2 Y2 Ẏ ( )2 Ẏ- (Ẏ- )2

55 10 550 3025 100 10.5 -6.875 47.26562 -6.375 40.64160 12 720 3600 144 12.5 -4.875 23.76562 -4.375 19.14185 28 2380 7225 784 22.5 11.125 123.76562 5.625 31.64175 24 1800 5625 576 18.5 7.125 50.76562 1.625 2.64180 18 1440 6400 324 20.5 1.125 1.26562 3.625 13.14185 16 1360 7225 256 22.5 -0.875 0.76562 5.625 31.64165 15 975 4225 225 14.5 -1.875 3.51562 -2.375 5.64160 12 720 3600 144 12.5 -4.875 23.76562 -4.375 19.141565 135 9945 40925 2553 0 274.875 0 163.628

The Correlation is: r =

=

= =.7748

Here r = .7748 so we can say that there are some positive relationship.

Hypothesis testing: Here, n=8 r = .7748 v=8-2=6

So, our null hypothesis is: And the alternative is: P0=0

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Business Statistics (BUS 505) Assignment 10

We reject H0 if, tv = > tv, or tv = < - tv,

= >

= 3.00 > 2.447 So we are reject null hypothesis at 5% level, and we can accept r = 0.7748

Linear Regression:Y= a + b x

Y=1.88757+(.4018) X

a = - b = 16.875 - (0.0895) (70.625) =1.88757

b = = = =0.4018

R2= = =.5952=60%

Page 23 of 23