In a small town of 5,832 people, the mayor wants to determine the proportion of voters who would support an increase to the food tax. An assistant to the mayor decides to survey 1,000 randomly chosen people to construct a 90% confidence interval for the true proportion of people who would support the increase in food tax. Of the sample, 363 people say they would support the increase. Are the conditions for inference met?

Yes, the conditions for inference are met.
No, the 10% condition is not met.
No, the randomness condition is not met.
No, the Large Counts Condition is not met.

Answer:

No, the 10% condition is not met is the answer.

1,000/5,832 is 0.1714, or ~17%, which is more than 10% of the population.

No, the 10% condition is not met.

Ratio:

'Ratio is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another.'

Proportion:

'A proportion is an equation in which two ratios are set equal to each other.'

According to the given problem,

Total number of people in the town = 5832

Number of people to be surveyed = 1000

Ratio of number of people chosen to the total population = [tex]\frac{1000}{5832}[/tex]

                                                                                                 = 0.17

Therefore percentage of people to be surveyed = 0.17 × 100

                                                                         = 17%, which is more than 10%

Hence, we can conclude that the 10% condition is not met.

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