Question

Medical: Red Blood Cell Volume 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 m 5 28 ml/kg (Reference: Laboratory and Diagnostic Tests by F. Fischbach). Red blood cell volume that is too low or too high can indicate a medical problem (see reference). Suppose that Roger has had seven blood tests, and the red blood cell volumes were
32 25 41 35 30 37 29

The sample mean is x < 32.7 ml/kg. Let x be a random variable that represents Roger’s red blood cell volume. Assume that x has a normal distribution and s 5 4.75. Do the data indicate that Roger’s red blood cell volume is different (either way) from m 5 28 ml/kg? Use a 0.01 level of significance.

please provide the following information.

(a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?
(b) Check Requirements What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. Compute the z value of the sample test statistic.
(c) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.
(d) 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 a?
(e) Interpret your conclusion in the context of the application.

For hypothesis testing, answer using the following steps…

Step 1: Write the hypothesis statements, identify which hypothesis is the claim, and the type of test you need to complete (left, right, twotail). State the level of significance.

Step 2: Check requirements (use the provided flowchart), state the calculator test you are using, and calculate the appropriate standardized test statistic (clearly identify the standardized test statistic by boxing or circling it).

Step 3: Make a properly labeled and shaded sketch using the standardized test statistic value. State and label the associated pvalue.

Step 4: Conclusion (make a decision) – your conclusion must include supporting evidence (refer to the decision rules on pg. 446).

Step 5: Interpretation (Based on our sample at the ______% level of significance, there is/is not enough evidence to support/reject the claim that state the claim.)

Answer 1

The provided sample mean is Xˉ=32.7

and the sample standard deviation is s = 4.75,

and the sample size is n = 7.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ = 28

Ha: μ ≠ 28

This corresponds to a two-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.01,

and the critical value for a two-tailed test is

t_c = 3.707.

The rejection region for this two-tailed test is

R={t:∣t∣>3.707}

(3) Test Statistics

The t-statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that

∣t∣ = 2.618 ≤  tc  ​=3.707,

it is then concluded that the null hypothesis is not rejected.

Using the P-value approach:

The p-value is p = 0.0397,

and since p  = 0.0397 ≥ 0.01,

it is concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean μ is different than 28, at the 0.01 significance level.

Confidence Interval

The 99% confidence interval is 26.044 < μ< 39.356.

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