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In a survey of 1,250 Filipino adults, 450 of them said that their favorite sport to watch is football. Using a confidence level of 90%, find a point estimate for the population proportion of Filipino adults who say their favorite sport to watch is football.

A. With 90% confidence, we can say that the proportion of all Filipino adults who say football is their favorite sport to watch is between 33.8% and 38.2%.

B. With 90% confidence, we can say that the proportion of all Filipino adults who say football is their favorite sport to watch is between 34.2% and 32.2%.

C. With 90% confidence, we can say that the proportion of all Filipino adults who say football is their favorite sport to watch is between 338.0% and 382.0%.

D. With 90% confidence, we can say that the proportion of all Filipino adults who say football is their favorite sport to watch is between 43.2% and 23.2%.

Solution:

Answer :

With 90% confidence, we can say that the proportion of all Filipino adults who say football is their favorite sport to watch is between 33.8% and 38.2%.

How to determine the confidence interval

From the question, we have the following parameters that can be used in our computation:

N = 1250

x = 450

So, the proportion p is

p = 450/1250

Evaluate

p = 0.36

The standard error is then calculated as

E = √[(p * (1 - p)/n]

So, we have

E = √[(0.36 * (1 - 0.36)/1250]

Evaluate

E = 0.01358

The confidence interval is then calculated as

CI = p ± zE

So, we have

CI = 0.36 ± (1.645 * 0.01358)

CI = 0.36 ± 0.0223391

Evaluate

CI = 0.3376609 to 0.3823391

Rewrite as

CI = 33.8% to 0.38.2%

Hence, the confidence interval is (a) 33.8% to 0.38.2%

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