According to a recent Current Population Reports, the population distribution of

Question

According to a recent Current Population Reports, the population distribution of number of years of education for self-employed individuals in the United States has a mean of 13.8 and a standard deviation of 2.2 (a) Identify the variable number of self-employed individuals in the United States number of self-employed individuals number of educated individuals in the United States number of years of education (b) Find the mean and standard error of the sampling distribution of for a random sample of size 110 Mean = (1 decimal place) Standard Error = (3 decimal places) (c) Find the mean and standard error of the sampling distribution of X for a random sample of size 389 Mean (1 decimal place) Standard Error (d) Describe the effect of increasing n (3 decimal places) The mean increases The mean stays the same The mean decreases. The standard error increases. The standard error stays the same. The standard error decreases (e) If a sample of size 389 is selected from this population, what is the probability that the sample average will be less than 14? probability (3 decimal places)

Explanation / Answer

a) D -> number of years of education

b) Mean is same as population mean of 12.8 and Standard error is 2.2/sqt(110)=0.2098

c) Mean is same as population mean of 12.8 and Standard error is 2.2/sqt(389)=0.1115

Increasing N mean stays the same whereas the standard error decreases

d) P(x<14) = P(z<(14-13.8)/0.1115 )=P(z<1.79)

From normal distribution table we get 0.9633

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