Transcript Solutions

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 0.002 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 H0 and alternative
hypothesis Ha 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 0.0291.
(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 H0 and alternative
hypothesis Ha 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 0.0016.
(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.