Question 4

Question 2 Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took the following glucose readings from this horse (in mg/100 ml). 95 8 8 80 107 101 112 8 4 87 The sample mean is  x   ≈   94.3 . Let  x  be a random variable representing glucose readings taken from Gentle Ben. We may assume that  x  has a normal distribution, and we know from past experience that   = 12.5. The mean glucose level for horses should be   = 85 mg/100 ml. †  Do these data indicate that Gentle Ben has an overall average glucose level higher than 85? Use   = 0.05. (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? H 0 :   = 85;  H 1 :   < 85; left-tailed H 0 :   = 85;  H 1 :   > 85; right-tailed H 0 :   = 85;  H 1 :    ≠  85; two-tailed H 0 :   > 85;  H 1 :   = 85; right-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  . The standard normal, since we assume that  x  has a normal distribution with unknown  . The Student's  t , since we assume that  x  has a normal distribution with known  . The standard normal, since we assume that  x  has a normal distribution with known  . 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.     0.05 2.10 0.0179

A plot of the normal probability curve has a horizontal axis with values from −3 to 3. 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 2.1 and 3 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  ? At the   = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the   = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the   = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the   = 0.05 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 0.05 level to conclude that the horse's glucose is higher than 85 mg/100 ml. There is insufficient evidence at the 0.05 level to conclude that the horse's glucose is higher than 85 mg/100 ml.    

e. There is insufficient evidence at the 0.01 level to conclude that the storm is increasing above the severe rating.     

Question 4 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   = 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  41  patients with arthritis took the drug for 3 months. Blood tests showed that  x  =  8.6  with sample standard deviation  s  =  3.1 . 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. H 0 :   = 7.4;  H 1 :   < 7.4 H 0 :   > 7.4;  H 1 :   = 7.4     H 0 :   = 7.4;  H 1 :   > 7.4 H 0 :    ≠  7.4;  H 1 :   = 7.4 H 0 :   = 7.4;  H 1 :    ≠  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   is unknown. The Student's  t , since the sample size is large and   is known.  The standard normal, since the sample size is large and   is known. The Student's  t , since the sample size is large and   is unknown. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Estimate the  P -value. P -value > 0.100 0.050 <  P -value < 0.100 0.020 <  P -value < 0.050 0.010 <  P -value < 0.020 P -value < 0.010 Sketch the sampling distribution and show the area corresponding to the  P -value. 0.05 2.479

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 −2.48 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 2.48 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  ? At the   = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the   = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

At the   = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the   = 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.