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Directions: Draw the normal curve and shade the specific region show formulas  A random same of 200 business showed thatb120 of them ban smoking on their premises.  Finding a 95% confidence interval for the population portion of all the business ban smoking on their premises

Question

Directions: Draw the normal curve and shade the specific region show formulas

 

 

A random same of 200 business showed thatb120 of them ban smoking on their premises.  Finding a 95% confidence interval for the population portion of all the business ban smoking on their premises 

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Step 1

Confidence interval:

The (1-α) % confidence interval for proportion p is given by,

ptz
pxq<p<p+z
n
n
Here, p
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ptz pxq<p<p+z n n Here, p

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Step 2

Computing the 95% confidence interval for population proportion:

It was found that, 120 businesses were ban smoking on their premises out of the 200 businesses. That is, n=200 and the sample proportion, p-hat = 0.6 (=120/200). The confidence level is 95%. Therefore, the significance level, α = 0.05 and the z value corresponding to α/2 is 1.96.  The 95% confidence interval for population proportion is given by:

0.6 1.960.6)x (1-0.0) <p<0.6 1.96,/0.6)x (1-0.6)
200
200
0.6 0.0679 p<0.6 0.0679
0.5321p <0.6679
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0.6 1.960.6)x (1-0.0) <p<0.6 1.96,/0.6)x (1-0.6) 200 200 0.6 0.0679 p<0.6 0.0679 0.5321p <0.6679

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Step 3

Plotting the confidence interval on a normal curve:

The graph of...

95%
0.5321
0.6
0.6679
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95% 0.5321 0.6 0.6679

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