n a large population, 74% of the households have cable tv. a simple random sample of 100 households is to be contacted and the sample proportion computed. what is the mean and standard deviation of the sampling distribution of the sample proportions?

Respuesta :

0.0439 is the mean and standard deviation of the sampling distribution of the sample proportions .

What is standard deviation in math?

  • Your dataset's average level of variability is represented by the standard deviation.
  • It reveals the average deviation of each statistic from the mean.
  • A low standard deviation denotes that values are grouped close to the mean, whereas a large standard deviation shows that values are often far from the mean.

Given that,

p = 0.74

1 - p = 1 - 0.74 = 0.26

n = 100

The mean of the sampling distribution of proportion is ,

 μP =    p = 0.74

The standard deviation of the sampling distribution  is ,  

  σp = σ\sqrtp ( 1 - p ) / n

 σp = σ\sqrt (0.74 * 0.26) / 100 = 0.0439

σp = = 0.0439

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