. (10 Points) Let x be a random variable representing the Reb Blood Count (RBC) in millions of cells per cubic millimeter of whole blood. The x distribution is normal. For the population of healthy female adults, the mean of the x distribution is 4.8. Suppose a female patient had six lab tests taken with a sample mean xbar = 4.40 and a sample standard deviation of 0.28. Do the given data indicate that the population mean RBC for this patient is lower than 4.8? Use a = 0.05. To receive full credit, show all your work. Failure to show all your work will result in the deduction of 2 points from the question. Use P-values from the standard distribution Z table 5 and the Student's t distribution table 6. Do not calculate P-values.

a. Check requirements, is the X_bar distribution normal? Explain

b. State the null and alternate hypothesis:

c. Compute the sample test statistic:

d. For H₁, estimate the P-value of the test statistic:

e. Conclude the test:

f. Interpret the results: