
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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Total blood volume (in ml) per body weight (in kg) is important in medical research. For healthy adults, the red blood cell volume
30 | 25 | 43 | 34 | 32 | 39 | 28 |
The sample mean is x ≈ 33.0 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 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.
Compute the z 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.)
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 α?
State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?
H0: μ = 28 ml/kg; H1: μ ≠ 28 ml/kg; two-tailedH0: μ = 28 ml/kg; H1: μ > 28 ml/kg; right-tailed H0: μ = 28 ml/kg; H1: μ < 28 ml/kg; left-tailedH0: μ ≠ 28 ml/kg; H1: μ = 28 ml/kg; two-tailed
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
The Student's t, since n is large with unknown σ.The Student's t, since we assume that x has a normal distribution with known σ. The standard normal, since we assume that x has a normal distribution with known σ.The standard normal, since we assume that x has a normal distribution with unknown σ.
Compute the z 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.)
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 α?
At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
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