A research study aims to test the claim that a prolonged exposure to air pollution reduces the number of red blood cells (RBC) in children. A lab test is conducted to measure the RBC count from a group of children who are exposed to air pollution on a regular basis in a large city. Data contains the test results for the RBC count (in x1012/L) measured from these 46 children. According to prior experiments, the number of RBC in healthy children who are not exposed air pollution has a mean value of 4.48 and a standard deviation of 0.29 trillion cells per liter.
Use this data file for the following:
a) Calculate the mean (x#) and standard deviation (s#) of the RBC in this sample.
b) Determine whether a one-tail or a two-tail test is more appropriate and justify your decision. Based on that, formulate a null hypothesis H& and an alternative hypothesis H'. Express both hypotheses with symbols, u (population mean for RBC count) and u& and explain them verbally.
c) Determine whether to use t-test or z-test and calculate the test statistic t*+,, or z.
d) Use an appropriate significance level a of your choice and calculate either pvalue or critical thresholds to test your hypotheses. State your conclusion about the effect of air pollution on the RBC count in children based on this test.
RedCellCount [x10^2/L] 4.01 3.64 4.47 4.64 4.7 4.68 4.68 4.22 4.09 4.85 4.13 3.78 4.62 4.34 4.45 3.81 4.4 4.61 4.26 4.68 4.69 4.42 3.75 4.4 3.9 4.5 3.95 5.23 3.96 3.89 3.92 4.95 4.26 4.3 14.5 3.93 5.04 4.62 3.83 4.61 4.06 4.28 4.34 4.72 4.59 4.3