stats solutions danny

7/22/2019 Stats Solutions Danny

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1. Poisson DistributionProblem

Southwestern Electronics has developed a new calculator that performs a series of functions

not yet performed by any other calculator. The marketing department is planning to

demonstrate this calculator to a group of potential customers, but is worried about some

initial problems, which have resulted in 4 percent of the new calculators developing

mathematical inconsistencies. The marketing VP Is planning on randomly selecting a group

of calculators for this demonstration and is worried about the chances of selecting a

calculator that could start malfunctioning. He believes that whether or not a calculator

functions is a Bernoulli process and he is convinced that the probability of malfunction is

really about 0.04.

a. Assuming that the VP selects exactly 50 calculators to use in the demonstration, andusing the Poisson distribution as an approximation of the binomial, what is the chance of

getting at least three calculators that malfunction?

b. No calculators malfunctioning?Solution

n = 50

p = 0.04

= np = 2

= 0.13533

Formula: P(X=) =

P ( =0) =

= 0.13533

P ( =1) =

= 0.27066

P ( =2) =

= 0.27066

P ( =3) =

= 0.18044


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P ( 3) = 1 P ( 2)

= 1 [P ( =0) + P ( =1) + P ( =2)]

= 1 [0.13533 + 0.27066 +0.27066]

= 0.32335

Answer

a.) The chance of getting at least three calculators that malfunction is 32.33%b.) The chance of no calculators malfunctioning is 13.53%


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2. Hypothesis Testing (Single Population)Problem

General Electric has developed a new bulb whose design specifications call for a light output

of 960 lumens compared to an earlier model that produced only 750 lumens. The companys

data indicate that the standard deviation of light output for this type of bulb is 18.4 lumens.

From a sample of 20 new bulbs, the testing committee found an average light output of 954

lumens per bulb. At a 0.05 significance level, can General Electric conclude that its new bulb

is producing the specified 960 lumen output?

Solution

= 18.4

n = 20 = 954 = 960 = 0.05 = 960

= 960

< 960

= - 1.65

=

=

= - 1.45

Answer

Do not reject . The new bulb is meeting specifications.


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3. Hypothesis Testing (Single Population)Problem

BSNL provides telephone services in Coimbatore. According to the companys records the

average length of calls placed through the company is 11.44 minutes. The company wants to

check if the mean length of the current calls is different from 11.44 minutes. A sample of 150

such calls placed through this company gave a mean length of 12.71 minutes with a standard

deviation of 2.65 minutes. Can you conclude that the mean length of all current calls is

different from 11.44 minutes? Use = 0.05.

Solution

s = 2.65

n = 150 = 12.71 = 11.44 = 0.05

= 11.44

11.44

= 1.65

=

=

= 5.87

Answer

Reject . It is concluded that the mean length of current calls is different from 11.44minutes.


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4. Hypothesis Testing ( Two populations)Problem

A credit-insurance organization has developed a new high-tech method of training new

sales personnel. The company sampled 16 employees who were trained the original way and

found average daily sales to be $688 and the sample standard deviation was $32.63. They

also sampled 11 employees who were trained using the new method and found average

daily sales to be $ 706 and the sample standard deviation was $24.84. At alpha = 0.05, can

the company conclude that average daily sales have increased under the new plan?

Solution

n1 = 16 n2 = 11 n = n1 + n2 = 27

1 = 688 2 = 206

1 = 32.63 2 = 24.84

= 0.05

1 - 2 = 0

1 - 2 0

= - 1.708

=

=

= 885.64


6/6

=

=

= - 1.545

Answer

Do not reject . Average daily sales have not increased significantly.

stats solutions danny

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