Question

In an episode of the old school version of the game show Family Feud, 43 out of a random sample of 100 people said they pick their noses at red lights. Find a 95% confidence interval of the proportion of all people who pick their noses at red lights. Be sure to interpret your answer

Answer 1

`P_(95\%)=(0.333,0.527)`

Explanation:

From the question we are told that:

Sample size
`n=100`

Selected sample
`x=43`

Confidence Interval
`CI=95\%`

Significance Level
`\alpha=0.05`

Probability of picking nose is

`P=(x)/(n)`

`P=(43)/(100)`

`P=0.43`

Generally the equation for standard error is mathematically given by

`S.E=√(p*(1-p)){n}`

`S.E=√(0.4*(1-0.57)){100}`

`S.E=0.0495`

Therefore

The proportions 95\% interval is

`P_(95\%)=[P-1.96x SE(P),P+1.96*SE(P)]`

`P_(95\%)=(0.43-1.96*0.0495,0.43+1.96*0.045)`

`P_(95\%)=(0.333,0.527)`