Let x be a random variable that represents red bloodcell count (RBC) in millions of cells per cubic millimeter of wholeblood. Then x has a distribution that is approximatelynormal. For the population of healthy female adults, suppose themean of the x distribution is about 4.74. Suppose that afemale patient has taken six laboratory blood tests over the pastseveral months and that the RBC count data sent to the patient'sdoctor are as follows.

4.9

4.2

4.5

4.1

4.4

4.3

(i) Use a calculator with sample mean and standard deviationkeys to find x and s. (Round your answers to twodecimal places.)

x	=
s	=

(ii) Do the given data indicate that the population mean RBC countfor this patient is lower than 4.74? Use α = 0.05.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: μ < 4.74;H₁: μ = 4.74

H₀: μ = 4.74;H₁: μ < 4.74

    H₀: μ = 4.74;H₁: μ > 4.74

H₀: μ = 4.74;H₁: μ ≠ 4.74

H₀: μ > 4.74;H₁: μ = 4.74

(b) What sampling distribution will you use? Explain the rationalefor your choice of sampling distribution.

The Student's t, since we assume that x has anormal distribution and σ is known.

The Student's t, since we assume that x has anormal distribution and σ is unknown.

     The standard normal, since we assumethat x has a normal distribution and σ isunknown.

The standard normal, since we assume that x has anormal distribution and σ is known.

What is the value of the sample test statistic? (Round your answerto three decimal places.)


(c) Estimate the P-value.

P-value > 0.250

0.100 < P-value < 0.250

     0.050 < P-value <0.100

0.010 < P-value < 0.050

P-value < 0.010

(d) Based on your answers in parts (a) to (c), will you rejector fail to reject the null hypothesis? Are the data statisticallysignificant at level α?

At the α = 0.05 level, we reject the null hypothesisand conclude the data are statistically significant.

At the α = 0.05 level, we reject the null hypothesisand conclude the data are not statistically significant.

    At the α = 0.05 level, we fail toreject the null hypothesis and conclude the data are statisticallysignificant.

At the α = 0.05 level, we fail to reject the nullhypothesis and conclude the data are not statisticallysignificant.

(e) Interpret your conclusion in the context of theapplication.

There is sufficient evidence at the 0.05 level to conclude thatthe population mean RBC count for the patient is lower than4.74.

There is insufficient evidence at the 0.05 level to concludethat the population mean RBC count for the patient is lower than4.74