Question: In running a white cell count, a drop of blood from an individual is smeared thinly and evenly on a glass slide, stained with Wright’s stain, and examined under a microscope. Of 200 white cells counted, 125 were neutrophils, a white cell produced in the bone marrow whose function, in part, is to take up infective agents in the blood. Use MINITAB to answer parts (a) and (c).

(a) For this individual, estimate with 90% confidence, the true proportion of white blood cells that are neutrophils. (3 marks)

(b) In a normally healthy individual, the percentage of white blood cells that are neutrophils is between 60 to 70%. Based on the interval obtained in part (a), is there clear statistical evidence of a neutrophil imbalance in this individual? Explain. (4 marks)

(c) Suppose we are not content with the width of the confidence interval found in part (a). That is, we would like to estimate the true proportion of white blood cells that are neutrophils, more precisely. How many white blood cells do we need to sample, to estimate the true proportion of white blood cells that are neutrophils, to within 0.025 and with 90% confidence? (4 marks)