A Better Golf Club? (a) Since Mike is interested in being more consistent, the parameter of interest is the standard deviation of the distance he hits the ball when using the new 7-iron. (b) Because Mike wants to be more consistent, he wants the standard deviation of the distance he hits the ball to be smaller than 15 yards. Ho : = 15 Ha: < 15 (c) If the true standard deviation is 15 yards, then there is an approximate probability of that the sample standard deviation would be 10.9 yards or lower because of random chance alone. (d) Yes. Since the P-value is very small, random chance is not a plausible explanation for why the sample standard deviation was lower than 15 yards. Thus, there is convincing evidence that the true standard deviation with the new 7-iron is smaller. (e) Mike is more consistent when using the new 7-iron (i.e. the true standard deviation of distances when using the new 7-iron is less than 15 yards).

State the appropriate null hypothesis H 0 and alternative hypothesis H a in each case. Be sure to define your parameter each time. A Gallup Poll report on a national survey of 1028 teenagers revealed that 72% of teens said they seldom or never argue with their friends. Yvonne wonders whether this national result would be true in her large high school. So she surveys a random sample of 150 students at her school

Hypothesis: For Yvonne’s survey, 96 students in the sample said they rarely or never argue with friends. A significance test yields a P-value of (a) Interpret this result in context. (b) Do the data provide convincing evidence against the null hypothesis? Explain.

(a): If the proportion of students at Yvonne’s school who say they rarely or never argue with friends is really 0.72, there is a 2.91% chance of finding a sample of 150 students with a value of p that is as far from 0.72 as the sample value in either direction. (b): Yes. This outcome was fairly rare (only 2.91% chance of happening) so we would likely reject the null hypothesis. It appears that the percent of students at Yvonne’s school is different from the national percent.

State the appropriate null hypothesis H 0 and alternative hypothesis H a in each case. Be sure to define your parameter each time. Hemoglobin is a protein in red blood cells that carries oxygen from the lungs to body tissues. People with less than 12 grams of hemoglobin per deciliter of blood (g/dl) are anemic. A public health official in Jordan suspects that Jordanian children are at risk of anemia. He measures a random sample of 50 children.

Hypothesis: For the study of Jordanian children, the sample mean hemoglobin level was 11.3 g/dl and the sample standard deviation was 1.6 g/dl. A significance test yields a P-value of (a) Interpret the P-value in context. (b) What conclusion would you make if α = 0.05? α = 0.01? Justify your answer

(a) If the mean hemoglobin level of Jordanian children is really 12, there is a 0.16% chance of finding a sample of 50 children with a mean level of 11.3 or lower. (b) Since the P-value is less than both 0.05 and 0.01, we would reject the null hypothesis in both cases. It appears that Jordanian children have an average hemoglobin level that is less than 12 mg/dl.