Out of a sample of 970 car owners, you find 261 that made their purchase primarily based on brand loyalty. Step 1 of 2: If you are interested in the proportion of car owners that base their purchase on brand loyalty, what is the Standard Error of the Sample Proportion obtained from these data? (Round to 4 decimal places.)

Given Information:

Sampling size = n = 261

Required Information:

standard deviation of sample proportion = σp = ?

Answer:

standard deviation of sample proportion = 0.0142

Explanation:

The standard deviation for sample proportion is given by

σp = √p (1 - p) / n

Check if the condition np ≥ 10 or n (1 - p) ≥ 10 is satisfied

p = 261/970

p = 0.269

np = 970*0.269

np = 260.93

n (1 - p) = 970 * (1 - 0.269)

n (1 - p) = 709.07

Since 260.93 ≥ 10 and 709.07 ≥ 10 then the sampling proportion will have less variability meaning that the distribution of sample proportion will have a mean of almost same as population proportion.

σp = √p (1 - p) / n

σp = √0.269 (1 - 0.269) / 970

σp = √0.269 (0.731) / 970

σp = 0.0142

Therefore, the standard error of the sample proportion obtained from these data is 0.0142

The standard error of the sample proportion is 0.0142.

Step-by-step explanation:

Standard error of a sample proportion is given as sqrt[p (1-p) : n]

p is the sample proportion = 261/970 = 0.269

n is sample size = 970

Standard error = sqrt[p (1-p) : n] = sqrt[0.269 (1-0.269) : 970] = sqrt[2.0272*10^-4] = 0.0142 (to 4 decimal places)