In a random sample of 400 electrical components,100 are found to be defective.if the hypothesis is that 20% of the components are defective,what is the standard error of the sample proportion
Standard error = √(pq/n)
From your problem:
p = 100/400, q = 1 - p, and n = 400.
Convert all fractions to decimals.
I'll let you take it from here.
To calculate the standard error of the sample proportion, you can use the formula:
Standard Error = √((p*(1-p))/n)
Where:
- p is the estimated proportion (in this case, the assumed proportion of defective components, which is 20% or 0.20 as a decimal)
- n is the sample size (in this case, 400)
So, let's plug in the values and calculate:
p = 0.20
n = 400
Standard Error = √((0.20*(1-0.20))/400)
First, subtract p (proportion) from 1:
1 - 0.20 = 0.80
Next, multiply p by (1-p):
0.20 * 0.80 = 0.16
Now, divide the above result by the sample size:
0.16 / 400 = 0.0004
Finally, take the square root of the obtained result to calculate the standard error:
√0.0004 = 0.020
Therefore, the standard error of the sample proportion is 0.020 (or 2.0% as a percentage).