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 23 40 37 28 38 29 The sample mean is x = 32.714 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 from ? = 28 ml/kg? Use ? = 0.01. (a) What is the level of significance? State the null hypothesis H0 and the alternate hypothesis H1 . H0 : ? H1 : ? What kind of test is this? left-tailed testtwo-tailed test right-tailed test (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since we assume that x has a normal distribution with known ?.The Student's t, since n is small with unknown ?. Compute the sample test statistic based on your choice of the distribution. (Round your answer to two decimal places.) (c) Find the P-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value.Graph!!! 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. 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.

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 23 40 37 28 38 29 The sample mean is x = 32.714 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 from ? = 28 ml/kg? Use ? = 0.01. (a) What is the level of significance? State the null hypothesis H0 and the alternate hypothesis H1 . H0 : ? H1 : ? What kind of test is this? left-tailed testtwo-tailed test right-tailed test (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since we assume that x has a normal distribution with known ?.The Student's t, since n is small with unknown ?. Compute the sample test statistic based on your choice of the distribution. (Round your answer to two decimal places.) (c) Find the P-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value.Graph!!! 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. 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.

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Description: 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

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

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The sample mean is x = 32.714 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 from ? = 28 ml/kg? Use ? = 0.01.

(a) What is the level of significance?

State the null hypothesis

H₀

and the alternate hypothesis

H₁

H₀

: ?

H₁

: ?

What kind of test is this?

left-tailed testtwo-tailed test right-tailed test

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

The standard normal, since we assume that x has a normal distribution with known ?.The Student's t, since n is small with unknown ?.

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

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

Sketch the sampling distribution and show the area corresponding to the P-value.Graph!!!

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.

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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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