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Homework answers / question archive / 1)Total blood volume (in ml) per body weight (in kg) is important in medical research
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.31254337293927The 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 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 hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?
-H0: μ = 28 ml/kg; H1: μ ≠ 28 ml/kg; two-tailed
-H0: μ = 28 ml/kg; H1: μ > 28 ml/kg; right-tailed
-H0: μ ≠ 28 ml/kg; H1: μ = 28 ml/kg; two-tailed
-H0: μ = 28 ml/kg; H1: μ < 28 ml/kg; left-tailed
(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 unknown σ.
-The standard normal, since we assume that x has a normal distribution with known σ.
-The Student's t, since we assume that x has a normal distribution with known σ.
-The Student's t, since n is large with unknown σ.
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.)______
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.
(e) State your conclusion in the context of the application.
-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. ___________________________________________________________________________________________________________________
2.Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is μ = 7.4.† A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 31 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.5 with sample standard deviation s = 2.7. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood.
(a) What is the level of significance?______
State the null and alternate hypotheses.
-H0: μ ≠ 7.4; H1: μ = 7.4
-H0: μ > 7.4; H1: μ = 7.4
-H0: μ = 7.4; H1: μ < 7.4
-H0: μ = 7.4; H1: μ ≠ 7.4
-H0: μ = 7.4; H1: μ > 7.4
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
-The Student's t, since the sample size is large and σ is unknown.
-The standard normal, since the sample size is large and σ is unknown.
-The Student's t, since the sample size is large and σ is known.
-The standard normal, since the sample size is large and σ is known.
What is the value of the sample test statistic? (Round your answer to three 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.
(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 = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
-At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
-At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
-At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the application.
-There is sufficient evidence at the 0.05 level to conclude that the drug has changed the mean pH level of the blood.
-There is insufficient evidence at the 0.05 level to conclude that the drug has changed the mean pH level of the blood. ___________________________________________________________________________________________________________
Unfortunately, arsenic occurs naturally in some ground water†. A mean arsenic level of μ = 8.0 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 31 tests gave a sample mean of x = 7.2 ppb arsenic, with s = 3.0 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use α = 0.10.
(a) What is the level of significance?______
State the null and alternate hypotheses.
-H0: μ = 8 ppb; H1: μ > 8 ppb
-H0: μ = 8 ppb; H1: μ ≠ 8 ppb
-H0: μ < 8 ppb; H1: μ = 8 ppb
-H0: μ = 8 ppb; H1: μ < 8 ppb
-H0: μ > 8 ppb; H1: μ = 8 ppb
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
-The Student's t, since the sample size is large and σ is unknown.
-The standard normal, since the sample size is large and σ is unknown.
-The standard normal, since the sample size is large and σ is known.
-The Student's t, since the sample size is large and σ is known.
What is the value of the sample test statistic? (Round your answer to three 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.
(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 = 0.10 level, we reject the null hypothesis and conclude the data are statistically significant.
-At the α = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant.
-At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
-At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the application.
-There is sufficient evidence at the 0.10 level to conclude that the mean level of arsenic in the well is less than 8 ppb.
-There is insufficient evidence at the 0.10 level to conclude that the mean level of arsenic in the well is less than 8 ppb.
