Answer to Question #316425 in Statistics and Probability for Bless

Question

The Ghana Revenue Authority (GRA) publishes annual figures on individual income tax returns in

Statistics of Income, Individual Income Tax Returns. For the year 2009, the GRA reported that the mean

tax of individual income tax returns was GH₡ 10,319. In actuality, the GRA reported the mean tax of a

sample of 292,966 individual income tax returns from a total of more than 130 million such returns.

a. Identify the population under consideration.

b. Identify the variable under consideration.

c. Is the mean tax reported by the GRA a sample mean or the population mean?

d. Should we expect the mean tax , of the 292,966 returns sampled by the GRA to be exactly the

same as the mean tax, µ, of all individual income tax returns for 2009?

e. How can we answer questions about sampling error? For instance, is the sample mean tax reported

by the GRA likely to be within GH₡ 100 of the population mean tax, µ?

Answer 1

$a: population\,\,of\,\,130000000 returns\\b: income\,\,tax\,\,return\\c: it\,\,is\,\,sample\,\,mean\\d: no, it\,\,should\,\,not\,\,be\,\,the\,\,same\\e: the\,\,sample\,\,error\,\,is\,\,\frac{1}{\sqrt{292966}}\sigma =0.00184753\sigma \,\,of\,\,the\,\,population\,\,error\\it\,\,will\,\,be\,\,within\,\,100 of\,\,\mu \,\,if\,\,0.00184753\sigma <100\Rightarrow \sigma <54054,\\which\,\,seems\,\,to\,\,be\,\,true$