Question

For a population with a proportion equal to 0.32, calculate the standard error of the proportion for the following sample sizes. a) 30 b) 60 c) 90 a) Op (Round to four decimal places as needed.) b) Op = (Round to four decimal places as needed.) c) Op (Round to four decimal places as needed.)

Answer 1

For a population with a proportion of 0.32, the standard errors for sample sizes of 30, 60, and 90 are 0.0852, 0.0602, and 0.0492 respectively when rounded to four decimal places.

Step-by-step explanation:

The standard error of the proportion is calculated using the formula: SE = √(p(1-p)/n), where 'p' is the population proportion and 'n' is the sample size. Let's use this formula to calculate the standard error for the given population proportion of 0.32 with different sample sizes.

• For a sample size of 30: SE = √(0.32(1 - 0.32)/30) = √(0.2176/30) = √(0.00725333) = 0.0852 (rounded to four decimal places)
• For a sample size of 60: SE = √(0.32(1 - 0.32)/60) = √(0.2176/60) = √(0.00362667) = 0.0602 (rounded to four decimal places)
• For a sample size of 90: SE = √(0.32(1 - 0.32)/90) = √(0.2176/90) = √(0.00241778) = 0.0492 (rounded to four decimal places)