Total blood volume (in ml) per body weight (in kg) is important in medical resea
ID: 3150955 • Letter: T
Question
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. 34 27 42 33 32 37 28 The sample mean is x 33.3 ml/kg. Let x be a random variable that represents Roger's red blood cell volume. Assume that x has a normal distribution and = 4.75. Do the data indicate that Roger's red blood cell volume is different (either way) from = 28 ml/kg? Use a 0.01 level of significance.
(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) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.?
What is the value of the sample test statistic? (Round your answer to two decimal places.)?
(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)?
Explanation / Answer
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. 34 27 42 33 32 37 28 The sample mean is x 33.3 ml/kg. Let x be a random variable that represents Roger's red blood cell volume. Assume that x has a normal distribution and = 4.75. Do the data indicate that Roger's red blood cell volume is different (either way) from = 28 ml/kg? Use a 0.01 level of significance.
(a) What is the level of significance?
The level of significance or alpha value is given as 0.01 or 1%.
State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?
Null hypothesis: H0: µ = 28
Alternative hypothesis: Ha: µ 28
This is a two tailed test.
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.?
Here, we have to use the z-distribution or normal distribution because we are given the population standard deviation.
What is the value of the sample test statistic? (Round your answer to two decimal places.)?
The formula for test statistic is given as below:
Test statistic = Z = (sample mean – population mean) / [Population SD / sqrt(n)]
Test statistic = Z = (33.3 – 28) / [ 4.75 / sqrt(7)]
Test statistic = Z = 2.95
(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)?
p-value = 0.0032 by using the z-table or normal distribution.
Z Test of Hypothesis for the Mean
Data
Null Hypothesis m=
28
Level of Significance
0.05
Population Standard Deviation
4.75
Sample Size
7
Sample Mean
33.3
Intermediate Calculations
Standard Error of the Mean
1.7953
Z Test Statistic
2.9521
Two-Tail Test
Lower Critical Value
-1.9600
Upper Critical Value
1.9600
p-Value
0.0032
Reject the null hypothesis
Z Test of Hypothesis for the Mean
Data
Null Hypothesis m=
28
Level of Significance
0.05
Population Standard Deviation
4.75
Sample Size
7
Sample Mean
33.3
Intermediate Calculations
Standard Error of the Mean
1.7953
Z Test Statistic
2.9521
Two-Tail Test
Lower Critical Value
-1.9600
Upper Critical Value
1.9600
p-Value
0.0032
Reject the null hypothesis