Question

Withdrawal symptoms may occur when a person using a painkiker stops using it. For a certain, widely taken painkiles, withdrawal symptoms occur in 12% of people who have stopped using the painiller. Suppose that we will take a random sample of 8 people who have stopped using the painkiler. Let p^​ represent the proportion of people from the sample who experienced withdrawal symptoms. Cansider the sampling distribution of the sample proportian p^​. Complete the following. Carry your intermediate computations to four or more decimal plsces. White your answers with two decimal places, rounding if needed. (a) Find μp​ (the mean of the sampling distribution of the sample proportion). (b) Find σa an ​ (the standard deviation of the sampling distribution of the sample proportion).

Answer 1

Step-by-step explanation:

To find the mean (μp) and standard deviation (σp) of the sampling distribution of the sample proportion, we can use the following formulas:

(a) Mean of the sampling distribution of the sample proportion:

μp = p

(b) Standard deviation of the sampling distribution of the sample proportion:

σp = sqrt((p * (1 - p)) / n)

Given that the proportion of people who experience withdrawal symptoms (p) is 12% or 0.12, and the sample size (n) is 8, we can calculate:

(a) Mean (μp):

μp = p = 0.12

(b) Standard deviation (σp):

σp = sqrt((p * (1 - p)) / n)

= sqrt((0.12 * (1 - 0.12)) / 8)

= sqrt(0.10608 / 8)

= sqrt(0.01326)

≈ 0.1151

Therefore, the answers are:

(a) μp = 0.12

(b) σp ≈ 0.1151