Of the 550 people surveyed about their habit of drinking soda, 242 indicated that they drink...

Of the 550 people surveyed about their habit of drinking soda, 242 indicated that they drink soda everyday. Determine the lower bound of the 99% confidence interval of the true proportion of the people who drink soda everyday.

Write your answer with 4 decimal places.

Solutions

Expert Solution

Solution :

Given that,

n = 550

x = 242

= x / n = 0.44

1 - = 1 - 0.44 = 0.56

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

Margin of error = E = Z_{/ 2} * $\sqrt$ [( * (1 - ) / n]

= 2.576 * $\sqrt$ [(0.44 * 0.56) / 550]

= 0.0545

A 99% confidence interval for population proportion p is ,

- E < P < + E

0.44 - 0.0545 < p < 0.44 + 0.0545

0.3855 < p < 0.4945

(0.3855, 0.4945)

orchestra answered 1 year ago

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