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 normal. For the population of healthy female adults, suppose the mean of the x distribution is about 4.74. 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 IN USE SALT ) Use a calculator with sample mean and standard deviation keys to find and s. (Round your answers to two decimal places.) (= (1) Do the given data indicate that the population mean RBC count for this patient is lower than 4.747 U = 0.05. (a) What is the level of significance? State the null and alternate hypotheses O HO = 4.74; H> 4.74 OH = 4.74; H4.74 OH! < 4.74; M = 4.74 Ho! 4.74; Hy < 4.74 Hl> 4.74; 4.74 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution The Student's t, since we assume that has a normal distribution and is known The standard normal, since we assume that has a normal distribution and is unknown The standard normal, since we assume that has a normal distribution and is known 12 PM

Answer 1

Given X: Random Versable that represent Red blood cell count 44.74 X: 4.9 4.2 4.5 4.1 4.4 SX 26.4 - 4.4 6 8(X;-*) 10.4 - 0.2828 not S=0.28 0 -0.05 9 Significance level = 0.05 Hypothesis Hoi l=4.74 ; Hi: 4<4.74 ..option 4th is correct. b Here n< 30 -0.34 option second is corect The Standard normal, since we assume x has normal distribution and 6 is unknown. : student's t-test is one sample t test is used. Test statistic t- X-4 4.4 - 4,74 Slin 0.28|56 0.143 t-2.975 3 p-value Plts-lt tal-Plt <-|-2.9951) = P(t< 2.975) = 0. 0155 option 4th ir correct 0.010 < 0.016=p-value <0.050 0.010 <p-value 0.00 Here povalue <a, Reject Ho conclusion: Population mean RBC Count for this patient is lower than 4.74