Question

Week # Revenue Print Ad TV Ad

1 $20,000 $ 3,100 $ 4,100

2 $22,000 $ 2,600 $ 4,200

3 $18,000 $ 2,800 $ 4,500

4 $21,000 $ 3,300 $ 4,300

5 $20,500 $ 3,100 $ 4,000

6 $19,000 $ 2,900 $ 3,700

7 $17,500 $ 2,500 $ 3,500

8 $21,225 $ 2,800 $ 3,600

9 $23,148 $ 3,000 $ 4,100

10 $22,865 $ 3,100 $ 4,400

11 $18,596 $ 2,600 $ 3,700

12 $17,432 $ 2,500 $ 3,100

Determine a 95% and 99% confidence interval that the revenue will exceed $20,000. The sample proportion will come from the data given but the confidence interval should be for calculation based on a year of data.

Answer 1

Here we are to calculate the 95% and 99% Confidence interval for Sample proportion of Revenue from the given data.

Here the Sample size is n=12

Let ,the No. of Revenues that will exceed $20000 is denoted by a R.V X

The Proportion of the Revenues Exceeding $20000(Sample proportion) p is=x/n =6/12

Now,For the confidence level 95%

= 100% -( level of Confidence) =100 -95 =5%

Now,For the confidence level 99%

= 100% -( level of Confidence) =100 - 99=1%

Now the Formula for the Confidence Interval of the Sample proportion is given by,

where is calculated from normal table.

For   =0.05

For   =0.01

(The values of These are calculated from Normal Table)

p=0.5

I.e,

So, the 95% Confidence Interval for the population proportion is:

Lower Bound =0.5-1.9560*0.1443 =0.2178

Upper Bound =0.5+1.9560*0.1443 =0.7823

So, the 99% Confidence Interval for the population proportion is:

Lower Bound =0.5-2.576*0.1443 =0.1283

Upper Bound =0.5+2.576*0.1443 =0.8717