Question

1st You are given the data in the table below;
12   12    18   18    21    27    7    14
21 19    17   10    20    23   16     9
Requirement. Describe the steps you would take to construct the boxplot that fits these data 

2nd
The Statistics Bureau surveyed 100 university students and found that 20% had gym membership
Requirements. Describe the methodology you would use to find the 95% confidence interval for the proportion of the population that has gym membership

3rd
You are given the data in the table below;
12   12    18   18    21    27    7    14
21 19    17   10    20    23   16     9
Requirement. Describe the steps you would take to construct the boxplot that fits these data 

Answer 1

Q1:

5 point summary:

Minimum = 7

First quartile, Q1 = (4th+5th)/2 value of sorted data = 12

Median = 0.5(n+1)th value = 8.5th value of sorted data = 17.5

Third quartile, Q3 = (12th+13th)/2 value of sorted data = 20.5

Maximum = 27

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Q2: n = 100, p̂ = 0.20

95% Confidence interval :

At α = 0.05, two tailed critical value, z_c = NORM.S.INV(0.05/2) = 1.960

Lower Bound = p̂ - z_c*√(p̂ *(1- p̂)/n) = 0.2 - 1.96 *√(0.2*0.8/100) = 0.122

Upper Bound = p̂ + z_c*√(p̂ *(1- p̂)/n) = 0.2 + 1.96 *√(0.2*0.8/100) = 0.278

0.122 < p < 0.278