6 Consider a situation in which a random sample of 1000 adults is surveyed and the proportion that primarily buys organic vegetables is found. If a new random sample of 1000 adults is taken from the same population, explain whether each of the following would change: a. The population proportion, p. b. The sample proportion, p^. c. The standard deviation of p^. d. The standard error of p^. e. The sampling distribution of p^, including its shape, mean, and standard deviation.

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Mathematics

Travis

30 August, 20:45

6 Consider a situation in which a random sample of 1000 adults is surveyed and the proportion that primarily buys organic vegetables is found. If a new random sample of 1000 adults is taken from the same population, explain whether each of the following would change: a. The population proportion, p. b. The sample proportion, p^. c. The standard deviation of p^. d. The standard error of p^. e. The sampling distribution of p^, including its shape, mean, and standard deviation.

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Brooks Aguilar · Answer 1

In the Step-by-step explanation.

Step-by-step explanation:

If a new sample is taken out of the same population,

a. The population proportion, p will not change. It is an unknown value that is estimated with the statistics of the samples.

b. The sample proportion, p^ is expected to change, because it is a new sample that has its own statistic value that may or may not be equal to the first sample.

c. The standard deviation of p^ is expected to change, because it depends on the sample and its size.

d. The standard error of p^ will change, because it depends on the sample.

e. The sampling distribution of p^, including its shape, mean, and standard deviation, will not change, because it is estimated with the data of the previous sample and it is supposed to be a property of the population and the sample size. Although the new information can be used to review the sample mean and standard deviation.