## Task – Global Homework Experts

Task 1 experiment with the files in the week 3 lecture section
generate random samples and summarize them

Question 1

Based on the screen shot below

1. What the excel function =COUNTIF(B5#,”yes”) return (what is the output)
2. What the excel function =COUNTA(B5#) return (what is the output)
3. Using the answer to part A) and Part B) to calculate the sampling population proportion

Note discussion of sampling populations is given in the video

note that video will start playing at time 380s if you watch from I start with a totally blank worksheet and make samples using the screenshot above

Note that there is a blue rectangle around the cell range B5:B9 so B5# refers to the cell range
B5:B9
A) 4 yes
B) there are 5 non empty cells in the array B5#
C) sampling population proportion 4/5=0.8

Question 2

If you use B6# as a sampling population what is the population proportion of yes

Population proportion p=54882/100000= 0.54882

Question 3

If you consider all of F7# as a single sample what is the sample proportion of yes

Sample proportion

Question 4

If you consider all of F7# as a single sample what is the sample proportion of yes

Sample proportion

General understanding of a measures of central tendency (the mean ) and a measure of spread (the standard deviation)

• What the sample size n, sample mean and sample standard deviation s of the sample
 Report Mark out of 20 7 13 10

Answer  you have quantitative variable size  n=3

Sample average (mean)

Sample standard deviation

• Given the 4 samples of data below and answer the following questions without formula (the answer is obvious and you don’t need the formula if you understand that standard deviation measures how far the points are from the average)

Sample 1: 100   100    100
Sample 2:   50    100    150
Sample 3:   90    100    110

Sample 4:  200   200    200

1. What is the mean of Sample 1
2. What is the standard deviation of Sample 1
3. Compare the mean and standard deviation of Sample 1 and Sample 2
4. Compare the mean and standard deviation of Sample 1 and Sample 4

Answer: mean of sample 1 is 100 and the standard deviation is 0

Sample 1 and 2 have the same mean but sample 2 must have a higher standard deviation,

Sample 1 and sample 2 have the same spread (standard deviation is 0) however sample 2 has a higher mean

• If 80 out of 100 Australians are scared of Donald Trump what is the sample proportion

As simpler example
If I  ask 5 people if they are scared of Donald Trump and the answers are the following dataset with 1 categorical variable

 Are you scared of trump ? Yes Yes No Yes No

You cannot find average but the proportion that are scared 3/5=0.6

5%   5 per cent   5/100=0.05

Harder Multiple choice
question 1

1. The heights of 100,000 females have heights summarized by the following histogram

The distribution of heights is symmetric with mean 175 and median 175
(the mean and median must be the same because it is symmetric)
How many females have a height between 165 and 185

A)8,400   B)7,000    C)2,000   D)1,0000

The blue  section must be 8% (the average is an axis of symmetry for the graph)
so the middle section is 100%-8%-8%=84%    84% of 10,000 is 8,400

Question 2

Complete the following table

 Height X round(height/5,0)*5      Height rounded to the nearest 5 174 175 182 180 183 185 187 185 168

Multiples of 5 are 0,5,10,15,20,25

Multiple choice fill in the blank

A)195
B)165
C)170
D)None of the above