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 μ = 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.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 σ = 4.75. Do the data indicate that Roger's red blood cell volume is different (either way) from μ = 28 ml/kg? Use a 0.01 level of significance. a) What is the level of Significance? State the null and alternate hypothesis. 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? c)Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-Value. d)Based on your answer to part (a) and (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? e)State your conclusion in the context of the application.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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 μ = 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.
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
a) What is the level of Significance? State the null and alternate hypothesis. 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?
c)Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-Value.
d)Based on your answer to part (a) and (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a?
e)State your conclusion in the context of the application.
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