Question

In: Statistics and Probability

The Food Marketing Institute and Nielsen reported that 49% of U.S. consumers shop for consumer package...

The Food Marketing Institute and Nielsen reported that 49% of U.S. consumers shop for consumer package goods products online. Assume the population proportion is p=0.49 and a sample of 500 consumers will be selected from the population.

Calculate the expected value and the standard error for the sampling distribution of p ̅, the sample proportion of consumers who shop for consumer package goods product online.

Describe the sampling distribution of p ̅. Draw a graph of this probability distribution with its mean and standard deviation.

What is the probability that the sample proportion will be greater than 0.52?

What is the probability that the sample proportion will be within ±0.02 of the population proportion?

Answer part d for a sample of 1000 households.

Solutions

Expert Solution

The expected value and the standard error for the sampling distribution of

The expected value is obtained using the following formula,

The standard error is obtained using the following formula,

Sampling distribution of

The sample proportion is normally distributed with

The probability that the sample proportion will be greater than 0.52

The probability is obtained by calculating the z score,

From the z distribution table,

The probability that the sample proportion will be within 0.02 of the population proportion

The probability is obtained by calculating the z score,

From the z distribution table,

For a sample of 1000 households.

Now, the probability is,

From the z distribution table,

orchestra answered 1 year ago
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