Question

A survey asks a random sample of 1500 adults in Ohio if they support an increase in the state sales tax from 5% to 6%, with the additional revenue going to education. Let P denote the proportion in the sample who say they support the increase. Suppose that 11% of all adults in Ohio support the increase. The standard deviation of the sampling distribution is..? Round your answer to four decimal places.

Answer 1

To calculate the standard deviation of the sampling distribution for the proportion of adults in Ohio who support an increase in sales tax, we use the formula √[p(1-p)/n] with p = 0.11 and n = 1500, resulting in a standard deviation of approximately 0.0081.

Step-by-step explanation:

To determine the standard deviation of the sampling distribution of the proportion (denoted as P), we can use the formula for the standard deviation of a sample proportion when the population proportion is known. The formula is √[p(1-p)/n], where p represents the true population proportion, and n is the sample size.

Given that 11% (or 0.11) of all adults in Ohio support the increase, and our sample size (n) is 1500, we plug these values into our formula for standard deviation:

√[0.11(1-0.11)/1500] = √[0.11*0.89/1500] = √[0.0979/1500] = √[0.00006527] ≈ 0.0081.

Therefore, the standard deviation of the sampling distribution for P is approximately 0.0081, rounded to four decimal places.

Answer 2

0.0081.

Step-by-step explanation:

Here, it is provided that the p = 0.11, n = 1500

The standard deviation of the sampling distribution can be calculated as:

Standard deviation of the sampling distribution

`\sqrt{(p(1-p))/(n) } \\\sqrt{(0.11(1-0.11))/(1500) } \\\\0.0081`

Hence, the required answer is 0.0081.