Letxbe a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Thenxhas a distribution that is approximately normal. For the population of healthy female adults, suppose the mean of thexdistribution is about4.80. 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

Do the given data indicate that the population mean RBC count for this patient is lower than4.80?

(a) Use= 0.05.(a) What is the level of significance?

State the null and alternate hypotheses.

• H₀:= 4.8;H₁:4.8
• H₀:> 4.8;H₁:= 4.8
• H₀:= 4.8;H₁:> 4.8
• H₀:= 4.8;H₁:< 4.8
• H₀:< 4.8;H₁:= 4.8

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

• 1. The standard normal, since we assume thatxhas a normal distribution andis known.
• 2. The Student'st, since we assume thatxhas a normal distribution andis known.
• 3. The Student'st, since we assume thatxhas a normal distribution andis unknown.
• 4. The standard normal, since we assume thatxhas a normal distribution andis unknown.

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

(d) Estimate theP-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

(e) Sketch the sampling distribution and show the area corresponding to theP-value.

(f) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level?

• 1. At the= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
• 2. At the= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
• 3. At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
• 4. At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(g) Interpret your conclusion in the context of the application.

• 1. There is sufficient evidence at the 0.05 level to conclude that the population mean RBC count for the patient is lower than 4.80.
• 2. There is insufficient evidence at the 0.05 level to conclude that the population mean RBC count for the patient is lower than 4.80.