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(Solved) Problem Set 3 Due on Friday, March 10, 2017, 12PM 1. Quality Progress reports on improvements in customer satisfaction and loyalty made by OCBC. A

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Problem Set 3

Due on Friday, March 10, 2017, 12PM 1. Quality Progress reports on improvements in customer satisfaction and loyalty made by OCBC. A key measure of customer satisfaction is the

response (on a scale from 1 to 10, 10 being most satised) to the question:

Considering all the the business you do with OCBC, what is your overall

satisfaction with OCBC?

(a) Historically the % of OCBC customers choosing a score of 9 or more

(extremely satised) is 48%. Suppose we wish to use a survey of 350 OCBC customers to justify the claim that more than 48% of all

current OCBC customers are extremely satised. The survey nds

that 189 of 350 customers rate 9 or more. Compute the probability

of observing a sample proportion greater than or equal to .54.

(b) Based on the probability you computed in part (a) would you conclude that more than 48% of current OCBC customers are extremely

satised? Explain.

(c) Find the probability that the sample proportion from the sample of

350 OCBC customers would be within

i. 3 percentage points of the population proportion.

ii. 6 percentage points of the population proportion.

(d) In 418 telephone interviews conducted, 67% of the respondents gave

a high rating for overall satisfaction.

i. Calculate a 99% condence interval for the proportion of all customers that are extremely satised.

ii. Can we be 99% condent that more than 60% of all customers

are extremely satised.

2. A computer supply house receives a large shipment of ash drives each

week. Past experience shows that the number of aws per drive is either

0, 1, 2 or 3 with probabilities .65, .2, .1 and .05 respectively.

(a) Calculate the mean and the standard deviation of the number of

aws.

(b) Suppose we select a sample of 100 ash drives. What is the distribution of the mean number of aws. Explain. 1 (c) A shipment is rejected if the mean number of aws per drive for a

sample of 100 is greater than .75. Suppose the actual number of aws

per drive in this weeks shipment is .55. What is the probability that

this shipment will be rejected.

3. Each day a manufacturing plant receives a large shipment of drums of

Chemical ZX-900. These drums are suppose to have a mean ll of 50 gallons and a s.d. of .6 gallon.

(a) If we draw a sample of 100 drums from the shipment, what is the

probability that the average ll for the 100 drums is between 49.88

gallons and 50.12 gallons.

(b) The plant manager will reject a shipment if the average ll of 100

drums is less than 49.85 gallons. Suppose a shipment which has a mean ll of 50 gallons is received. What is the probability that this

shipment is rejected?

4. A company is considering a new bottle design for a popular soft drink

and takes a sample of 60 consumer ratings of this new bottle design. The

mean and the s.d of the 60 bottle design ratings are 30.35 and 3.1073

respectively. Compute a 95% condence interval for the mean. Interpret

this interval.

5. An ad agency output is described by nding the shares of dollar billing

volume coming from various media categories such as network TV, spot

TV, newspapers, radio and so forth.

(a) Suppose that a random sample of 400 advertising agencies gives an

average percentage share of billing volume from network TV equal

to 7.46% and assume that the population s.d. equals to 1.42%. Compute a 95% condence interval for the mean percentage share

of billing volume from network TV.

(b) Suppose that a random sample of 400 advertising agencies gives an

average percentage share of billing volume from spot TV equal to

12.44% and assume that the population s.d. equals to 1.55%. Compute a 95% condence interval for the mean percentage share of

billing volume from spot TV.

(c) Compare the intervals in (a) and (b). Does it appear that the mean

percentage share of billing volume from spot TV is greater than the

mean percentage share of billing volume from network TV? Explain.

6. Suppose we conduct a poll to estimate the proportion of voters who favour

a major presidential candidate. Assuming that 50% of the electorate could

be in favour of the candidate, determine the sample size needed so that we

are 95% condent that pË†, the sample proportion of all voters who favour athe candidate, is within a margin of error of .01 of 2 p.

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