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saul85 [17]
4 years ago
12

6. During an independent research, 2500 randomly selected people were interviewed whether they visit their dentist for a regular

dental checkup or not. Only 2000 gave a positive answer. Calculate a 95% two-sided confidence interval on the proportion of people who regularly have a dental checkup.
Mathematics
1 answer:
Sophie [7]4 years ago
8 0

Answer:

0.80+/- 0.016

(0.784, 0.816)

The 95% confidence interval on the proportion of people who regularly have a dental checkup is = (0.784, 0.816)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

p+/-z√(p(1-p)/n)

Given that;

Proportion p = 2000/2500 = 0.80

Number of samples n = 2500

Confidence interval = 95%

z-value(at 95% confidence) = 1.96

Substituting the values we have;

0.80+/- 1.96√(0.80(1-0.80)/2500)

0.80+/- 1.96√(0.000064)

0.80+/- 0.01568

0.80+/- 0.016

(0.784, 0.816)

The 95% confidence interval on the proportion of people who regularly have a dental checkup is = (0.784, 0.816)

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Part b

The correlation coefficient is given by:

r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}  

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n=7 \sum x = 4210, \sum y = 49, \sum xy = 30095, \sum x^2 =2595100, \sum y^2 =354  

r=\frac{7(30095)-(4210)(49)}{\sqrt{[7(2595100) -(4210)^2][7(354) -(49)^2]}}=0.7503  

The determination coefficient is given by:

r^2 = 0.7503^2 = 0.563

Part c

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