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Whichsamplingtechniquehasbeenusedinthefollowingsituations?Ineachcase,firstdecideif itisrandomornon-randomsamplingandthenstatetheactualtechnique. (a)...

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Whichsamplingtechniquehasbeenusedinthefollowingsituations?Ineachcase,firstdecideif itisrandomornon-randomsamplingandthenstatetheactualtechnique. (a) Acoffeeshopcollectsdatafrom100customersontheircoffeepreferencesby interviewingevery25thcustomerthatentersthestoreuntiltheyhavedone100 interviews. (b) OnthefirstThursdayofeachmonth,apizzadeliveryshopphoneseverycustomer whohasorderedapizzabetween7pmand9pmtoaskthemaboutthepromptness ofdeliveryandqualityofthepizza. (c) A university runs a subject across three different campuses. To check for consistency between markers,theunitchairrandomlyselects10assignmentsfromeachcampusand checksforanyinconsistenciesinthemarking
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MIS770 Revision- Additional Exercises      Q1  Which sampling technique has been used in the following situations? In each case, first decide if  it is random or non-random sampling and then state the actual technique.    (a) A coffee shop collects data from 100 customers on their coffee preferences by  interviewing every 25th customer that enters the store until they have done 100  interviews.  (b) On the first Thursday of each month, a pizza delivery shop phones every customer  who has ordered a pizza between 7pm and 9pm to ask them about the promptness  of delivery and quality of the pizza.  (c) A  university  runs  a  subject  across  three  different  campuses.  To check for consistency  between  markers, the unit chair randomly selects 10 assignments from each campus and  checks for any inconsistencies in the marking.      Scenario: (Q2-Q6)    The data relate to a random sample of 150 supermarkets in the Foodmart chain. Due to a concern about  rising food costs, each of the stores in the survey were asked to determine the cost of a  given basket of  food items in their store on the 3rd of June 2014. Each store repeated the exercise   to determine the  cost of the exact same basket in their store on the 3rd June 2015.    Q2 The percentage change in the cost of the basket (%Change) is used to measure the annual increase  in the cost of the basket for each supermarket. Percentage change  can  be  compared  to  the  movement in the Food component of the Australian CPI over the same period.    (a) What would the variable of interest be in this case?    (b) What is the population of interest?    (c) In this context, what is meant by the sample?    (d) What would be the parameter to be estimated?    (e) What would be the sample statistic?        Q3      Calculate the sample size that would be required to estimate the average annual percentage change  in  the  cost  of  the  basket  for  all  supermarkets  to  within  0.2%  with  99%  confidence.  Assume ...

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Answered Same Day Dec 26, 2021

Solution

David answered on Dec 26 2021
129 Votes
1)
a)
A coffee shop collects data from 100 customers on their coffee preferences by interviewing every 25th
customer that enters the store until they have done 100 interviews.
Random – Systematic
)
On the first Thursday of each month, a pizza delivery shop phones every customer who has ordered a
pizza between 7pm and 9pm to ask them about the promptness of delivery and quality of the pizza.
Non-random – convenience
c)
A university runs a subject across three different campuses. To check for consistency between markers,
the unit chair randomly selects 10 assignments from each campus and checks for any inconsistencies in
the marking.
Random – stratified
Q2)
a) annual increase in the cost of the basket
) all supermarkets in Australian
c) 150 supermarkets in the Food-mart chain
d) annual increase in the cost of the basket for all supermarkets in Australian
e) annual increase in the cost of the basket for 150 supermarkets in the Food-mart chain
Q3)
n = z(a/2)^2*sd^2/ME^2
z(a/2)= 2.575829
n= =2.576^2*0.008^2/0.002^2

106.1724

106 (approx)
Q4)
a)
Arithmetic mean (i)
4.2563
Median (ii)
4.3000
Mode (iii)
4.0000
First Quartile (iv)
3.9000
Third Quartile (v)
4.5250
Range (vi)
2.6000
Inter Quartile Range (vii)
0.6250
Standard Deviation (Sample) (viii)
0.7933
Coefficient of Variation (Sample) (ix)
18.6380
)
skewness = -.165
for a negatively skewed data, mean < median < mode which is true here.
c)
median is the best measure of central tendency as data is skewed. Here median is 4.3
Q5)
Mean= 4.20%
Sd= 0.80%

a)
P(3%P(X<5%)-P(X<3%)

Z1 = =(5%-4.2%)/0.8% =1.00
Z2 = =(3%-4.2%)/0.8% =-1.50

P(X<5%)-P(X<3%)
p(Z<1)-p(z<-1.5)
=NORMSDIST(1)-NORMSDIST(-1.5)
0.774538

)
n= 16
P(4%P(X<5%)-P(X<4%)

Z1 = =(5%-4.2%)/(0.8%/SQRT(16)) 4.00
Z2 = =(3%-4.2%)/(0.8%/SQRT(16)) -6.00

P(X<5%)-P(X<4%)
p(Z<4)-p(z<-6)
=NORMSDIST(4)-NORMSDIST(-6)
0.999968

Q6)
Mean= 4.092
Sd= 0.795
n= 25

a)
95% ci
mean +- z(a/2)*(sd/sqrt(n))
lower =4.092-1.96*(0.795/SQRT(25)) =3.78036
upper =4.092+1.96*(0.795/SQRT(25)) =4.40364

)
I am 95% confident that estimated population mean for percentage change for all
supermarkets in the Food-mart chain lies in the interval [3.78, 4.40].
c)
Since the confidence interval doesn’t contain...
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