Total blood volume (in ml) per body weight (in kg) is important in medical research. For healthy adults, the red blood cell volume mean is about= 28 ml/kg.Red blood cell volume that is too low or too high can indicate a medical problem. Suppose that Roger has had seven blood tests, and the red blood cell volumes were as follows.30264337303928The sample mean isx=33.286ml/kg. Letxbe a random variable that represents Roger's red blood cell volume. Assume thatxhas a normal distribution and= 4.75.Do the data indicate that Roger's red blood cell volume is different from= 28 ml/kg?Use=0.01.(a) What is the level of significance?

State the null hypothesisH₀

and the alternate hypothesisH₁

.

H₀

:

H₁

:

What kind of test is this?

left-tailed testtwo-tailed testright-tailed test

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

The standard normal, since we assume thatxhas a normal distribution with known.The Student'st, sincenis small with unknown.

Compute the sample test statistic based on your choice of the distribution. (Round your answer to two decimal places.)

(c) Find theP-value. (Round your answer to four decimal places.)

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

(d) Based on your answers in the previous parts, state your decision. Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level?

At the= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) State your conclusion.

There is sufficient evidence at the 0.01 level to conclude that Roger's average red cell volume differs from the average for healthy adults.There is insufficient evidence at the 0.01 level to conclude that Roger's average red cell volume differs from the average for healthy adults.