You sample 52 people in India and observe that their average years of schooling

Question

You sample 52 people in India and observe that their average years of schooling is 6.7. You know the distribution of years of schooling in India has a standard deviation of 2.8. The distribution of years of schooling in India is not Normal.

a) What is the sampling standard deviation of the sample mean?

b) What is the sampling mean of the sample mean?

c) Calculate a 90% confidence interval for the mean number of years of schooling in India. Interpret the result.

d) Calculate a 95% confidence interval for the mean number of years of schooling in India. Interpret the result.

e) Calculate the 99% confidence interval for the mean number of years of schooling in India. Interpret the result.

Explanation / Answer

here as sample size is greater than 30 from central limit theorum we may consider that sampling distribution of mean would be normal

a) sampling standard deviation of the sample mean =population std deviation/(n)1/2 =2.8/(52)1/2 =0.3883

b)  sampling mean of the sample mean =population mean =6.7

c)

we have 90% confidence of finding sample mean with in interval 6.06 to 7.34.

d)

we have 95% confidence of finding sample mean with in interval 5.94 to 7.46.

e)

we have 99% confidence of finding sample mean with in interval 5.70 to 7.70.  

for 90 % CI value of z= 1.6449 margin of error E=z*std error                            = 0.639 lower confidence bound=sample mean-margin of error= 6.06 Upper confidence bound=sample mean +margin of error= 7.34

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