Department

Economics for Management StudiesCourse Code

MGEB12H3Professor

Vinh QuanLecture

1This

**preview**shows half of the first page. to view the full**2 pages of the document.**Department of Management, UTSC

MGEB12 Quantitative Methods in Economics II - Ass1 – Solution

Problem 1

(a) From output 95% 2-sided C.I:

72 – 2.4768 ≤ µ ≤ 72 + 2.4768 so 69.5232 ≤ µ ≤ 74.4768 so should not launch drink.

(b) For a 80% C.I. 100(1-α) = 80 get α = 0.2, d.f. = n – 1 = 25-1 = 24

n

s

tx

n

2

,1

α

−

±

→

25

0.6

0.72

1,.24

t

±

From

2/][

2

,11

α

α

=≥

−−

nn

ttP

→

1.][

1,.2424

=≥

ttP

From t-dist table get t24,0.1 = 1.318

C.I. is 72 ± 1.816 or 70.4184 ≤ µ ≤ 73.5816

(c)

Ho: µ = 75

Ha: μ ≠ 75

Reject Ho if t0 ≤ -tα/2 or t0 ≥ tα/2

ns

x

t/

0

0

µ

−

=

=

25/6

7572

−

= -2.5, d.f. = n – 1 = 25-1 = 24

From

2/][

2/

α

α

=≥

ttP

→ P[t24 ≥ t24,.005] = 0.005 get t24,.005 = 2.797

Is -2.5 ≤ -2.797 or -2.5 ≥ 2.797? No, so do not reject Ho. The mean rating is equal to 75.

Some sample recommendations:

(a) Increase sample size

(b) Take volunteers from other locations and not just in IC building to make sample more representative of

population.

(c) Make sure volunteers include different age

(d) Make sure volunteers include different background (eg, asian, black, etc.)

(e) Make sure volunteers include male and female.

(d)

Ho: µ≤ 75

Ha: μ > 75

Reject Ho if Z0 ≥ Zα , Test Statistic

n

x

Z/

0

0

σ

µ

−

=

=

25/5

75

−

x

, Zα = Z0.01 = 2.325

Reject Ho if Z0 ≥ Zα →

25/5

75

−

x

≥ 2.325 or

x

≥ 77.325

Therefore fail to reject Ho or commit type II error if

x

< 77.325

β = P[

x

< 77.325] = P[

x

≤ 77.325] due to

x

is continuous RV

P[

xx

xExEx

σσ

][325.77][

−

≤

−

] = P[

25/5

77325.77

/

−

≤

−

n

x

a

σ

µ

] = P[z ≤ .325]

= (.6255 + .6293) /2 = .6274

(e)

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