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 mu = 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 36 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.4 with sample standard deviation s = 2.9. 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: mu > 7.4; H1: mu = 7.4 H0: mu ≠ 7.4; H1: mu = 7.4    H0: mu = 7.4; H1: mu < 7.4 H0: mu = 7.4; H1: mu > 7.4 H0: mu = 7.4; H1: mu ≠ 7.4 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since the sample size is large and o is unknown. The Student's t, since the sample size is large and o is unknown.     The standard normal, since the sample size is large and o is known. The Student's t, since the sample size is large and o is known.   What is the value of the sample test statistic? (Round your answer to three decimal places.)   (c) Estimate the P-value. P-value > 0.150 0.100 < P-value < 0.150     0.050 < P-value < 0.100 0.020 < P-value < 0.050 P-value < 0.020   Sketch the sampling distribution and show the area corresponding to the P-value.   A plot of the Student's t-probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between −4 and −2.07 as well as the area under the curve between 2.07 and 4 are both shaded.   A plot of the Student's t-probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between 2.07 and 4 is shaded.   A plot of the Student's t-probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between −4 and −2.07 is shaded.   A plot of the Student's t-probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between −2.07 and 4 is shaded. (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 a? At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.     At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the a = 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.

Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma.+ Over a period of months, an adult male patient has taken eleven blood tests for uric acid. The mean concentration was x = 5.29 mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal, with o = 1.87 mg/dl. (a) Find a 95% confidence interval for the population mean concentration of uric acid in this patient's blood. What is the margin of error? (Round your answers to two decimal places.) lower limit upper limit margin of error (b) What conditions are necessary for your calculations? (Select all that apply.) o is known o is unknown normal distribution of uric acid O uniform distribution of uric acid On is large (c) Interpret your results in the context of this problem. O We are 5% confident that the true uric acid level for this patient falls within this interval. O We are 95% confident that the…

Ann thinks that there is a difference in quality of life between rural and urban living. She collects information from obituaries in newspapers from urban and rural towns in Idaho to see if there is a difference in life expectancy. A sample of 3 people from rural towns give a life expectancy of xr¯=79��¯=79 years with a standard deviation of sr=7.57��=7.57 years. A sample of 14 people from larger towns give xu¯=82��¯=82 years and su=5.48��=5.48 years. Does this provide evidence that people living in rural Idaho communities have different life expectancy than those in more urban communities? Use a 5% level of significance. (a) State the null and alternative hypotheses: (Type ‘‘mu_r′′‘‘��_�″ for the symbol μr�� , e.g. mu_rnot=mu_u��_����=��_� for the means are not equal, mu_r>mu_u��_�>��_� for the rural mean is larger, mu_r<mu_u��_�<��_� , for the rural mean is smaller. )H0�0 =  equation editor Equation Editor Ha�� =  equation editor Equation Editor   (b) The degree of…

Unfortunately, arsenic occurs naturally in some ground water.† A mean arsenic level of μ = 8.3 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 41 tests gave a sample mean of x = 7.3 ppb arsenic, with s = 2.4 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8.3 ppb? Use ? = 0.01.   (a) What is the level of significance?   State the null hypotheses  H0  and the alternate hypothesis  H1 . H0 : μ  ---Select--- < ≥ ≤ = > ≠   H1 : μ  ---Select--- < >  ≤ ≥ = ≠  (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. 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.     The standard normal, since the sample size is large and σ is unknown. The Student's t, since the…