Question

Let x be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normas For the population of healthy female adults, suppose the mean of the x distribution is about 4.76. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient's doctor are as follows. 4.9 4.2 4.5 4.1 4.4 4.3 A USE SALT (Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) CID) Do the given data indicate that the population mean RBC count for this patient is lower than 4.767 Use a -0.05. (a) What is the level of significance? State the null and alternate hypotheses. Ô Hp A = 4.7%; H: A+ 4,76 Mo: > 4.76; H: -4.76 0 Hp: = 4.76 Hi JA = 4,76 Ho! - 4.76; M: < 4.76 Mo: -4.76; H> 4.76 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution The standard normal, since we assume that has a normal distribution and is unknown The Student's t, since we assume that x has a normal distribution and is unknown The standard normal, since we assume that has a normal distribution and is known The Student's t, since we assume that has a normal distribution and is known

Answer 1

Given Samples are, X; - 4.9 4.2, 4.5, 4.1, 4.4, 4.3 ; ) Here, n = 6 2x 26.4 6 4.4 0.28 Vih-i 2 (x; -4)2 = Voros (1) level of significance = x 0.05 Let Mbe RBC the population mean to test whether we want M is less than 4.76 Ho: M = 4.76 ; Hii M < 4:76 의 The student's t, since we assume that x has a normal distribution and 6 is unknown. Test statistic, din (x M V6 (414-4.76 0.28 3 t -31149 af (-i) : 5 P[ tg <-3.149 P-value from t table 0.0127 0.010 < P-value <0.050

Clearly as p value less than 0.05

We Reject Ho at 0.05 level .

The given data indicates that the population mean RBC is lower than 4.76 .