Business Statistics 1B

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Business Statistics 1B

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QU E T

i

H0: i t t l

H1: R i t t

2. Cr i i l va l

-1)(c -1) = (2 -1)(3 -1) = 2

Leve l of s i if icance = 0.01 wh ich y iel s x2 cr it= 9.21034

The dec ision ru le is : R e ject H0 if x 2 calc > 9.21034

3. Ch i- q ared stat ist i

67 71.5 0.28363 58.5 0.34632 27.5 0.73618 22.5 0.911 11 09 9 0

X2 ca lc= 2.265

4. Dec isi

Do no t re ject H0.

5. Conc l sion

At the 0.01 level of s i nif icance, we can conc lude that there is insuff icient statistica l evidence

to infer that responses d iffer among b lue-collar, wh ite-collar and managers. R esponses are

uniform among the responden ts.


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QU E T 2

2.1

1. Hypothes is

H0: 30

H1: < 30

2. Cr it ica l Va l e

=0.05 n = 86 thus we use Z for the one s ided test

rejection region -1.645 acceptance region

Dec ision ru le: R e ject H0 if Z calc < -1.645

3. T est stat ist ic

4. Dec ision

Since Z ca lc (2.24) > Z cr itical value (-1.645), we do no t re ject H0

5. Conc l sion

The supermarke t s c laim that customers spend ha lf -an-hour or more carry ing ou t purchases isstatistically true a t 5% level of s ignif icance


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2.2.1Conf idence interva l C P =0.48 q = 0.52 n = 500 =0.05 for two s ides Z a/2= 1.96

We are 95% conf ident that the true propor tion of success is be tween 43.6% and 52.4%.

2.2.1Conf idence interva l P =0.48 q = 0.52 n = 1000 =0.05 for two s ides Z a/2= 1.96

We are 95% conf ident that the true propor tion of success is be tween 44.9% and 51.1%.

2.2.3Increas ing the samp le s i e increases the conf idence interva l


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Qu est ion 33.1

Golfer X2 Sk ier Y22450 6002500 3805 144780253860 14899600 3725 138756254528 20502784 2990 89401001944 3779136 4357 189834493166 10023556 5550 308025003275 10725625 4130 170569004490 201601003585 128522252950 870250030248 107648026 24557 104136599

Var iances

S1 2 (golfers) =

S2 2 (sk iers) =

S1 2 = 748482.3611

S2 2 = 725778.1667

1. Hypothes is

H0: H1:

2. Dec ision r u leDegree of freedom numera tor= 9 -1 = 8Degrees of freedom denom inator = 6 -1 = 5

= 0.05

F-cr itical = 4.82 (From F -Tab le)

R e ject H0 if F -stat 4.82

3. F -T estS1

2 / S2 2 = 748482.3611 /725778.1667 = 1.031

4. Dec isionSince F -stat = 1.031 < 4.82 we do no t re ject H0 and conc lude that the two

popu lation var iances are no t differen t.


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3.2

Samp le mean 1(go lfers) =3360.88Samp le mean 2(sk iers) =4092.83

1. Hypothes isH0 : H1 : 2. Dec ision R u le

df= 9+6 -2 = 13=0.01 therefore t-cr it = 3.012

R ule: R e ject H0 if t-calc 3.012or t-calc -3.012

3. Samp le stat ist ic

S2 =

= 739749.97

t-calc =

= -731.94 /453.306 = -1.61

4. Do no t re ject H0

5. Mean vaca tion expenses be tween go lfers and sk iers do no t diffe r a t 0.01 level of s ignif icance

Business Statistics 1B

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