Question

Out of 168 randomly selected adults in the United States who were surveyed, 89 exercise on a regular basis. Construct a 98 % confidence interval for the proportion of all adults in the United States who exercise on a regular basis. Round to three decimal places.

Answer 1

98 % confidence interval for the proportion of all adults in the United States who exercise on a regular basis is 0.440 < P < 0.619.

What does a statistical random sampling entail?

• A selection of participants from a population are chosen at random by the researcher using simple random sampling, a sort of probability sampling.
• Every person in the population has the same chance of being chosen. Then, data are gathered from as much of this randomly selected subgroup as possible.

P = x/n

= 89/168

= 0.53

α= 0.02

∴Zc = Zi - α/2

= 2.326

Now, C.I = P ± Zc * √[P(1-P)/n]

= 0.5 ± 2.326 * √[(0.53(1-0.53)) / 168

= (0.440, 0.619)

∴98% C.I. = 0.440 < P < 0.619

Hence, 98 % confidence interval for the proportion of all adults in the United States who exercise on a regular basis is 0.440 < P < 0.619.

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