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# Question (20 marks)(a) Let %z be the systematic sample mean We know that %, is an unbiased estimator off the NJ population mean. Show that Var(;) = "7152, (all...

## Question

###### Question (20 marks)(a) Let %z be the systematic sample mean We know that %, is an unbiased estimator off the NJ population mean. Show that Var(;) = "7152, (all symbols have their usual meaning) According to POPD Ltd; there were 118 Covid-19 cases reported in March 2020 in Kenya . The number of cases in each reporting region is listed below with the regions numbered from North to South and identified by numbers only:Region Number Number of CasesSuppose that public heath researcher had decide

Question (20 marks) (a) Let %z be the systematic sample mean We know that %, is an unbiased estimator off the NJ population mean. Show that Var(;) = "7152, (all symbols have their usual meaning) According to POPD Ltd; there were 118 Covid-19 cases reported in March 2020 in Kenya . The number of cases in each reporting region is listed below with the regions numbered from North to South and identified by numbers only: Region Number Number of Cases Suppose that public heath researcher had decided to estimate the total number of Covid-19 cases in Kenya in March 2020 not by contacting each ofthe N-l2 reporting regions; but by selecting One in-three systematic sample from the 12 regions. Selecting starting region number on the list at random from the numbers 1, 2 3, the sample includes that region and every third region thereafter on the list. (0) List every possible systematic sample that could be obtained with the design marks) To estimate the total number of cases XT (the true value is 118) the researcher multiplies the total number of cases in the sample by 3. Is this estimate unbiased for the population total (Xr) Justify your answer_ marks)(111) (jii What is the true variance of the researchers estimate? (3marks) For an estimate of the variance in pait (ii1) . the researcher used 12(12-4)52/4 where s" is the

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