Statistics Homework 10.3
#1 Several yearsago, the mean height of women 20 years of age or older was 63.7
inches. Suppose that a random sample of 45 women who are 20 years of age or older
today results in a mean height of 64.4 inches.
(a) State the appropriate null and alternative hypotheses to assess whether women are
taller today.
(b) Suppose theP-value for this test is 0.02 Explain what this value represents.
(c) Write a conclusion for this hypothesis test assuming an alpha=0.10 level of
significance.
For answers for a) and b) open picture
d)
(c) Write a conclusion for this hypothesis test assuming a=0.10 level of significance.
Reject the null hypothesis. There is sufficient evidence to conclude that the mean height
of women 20 years of age or older is greater today
#2 A college entrance exam company determined that a score of 20 on the mathematics
portion of the exam suggests that a student is ready forcollege-level mathematics. To
achieve thisgoal, the company recommends that students take a core curriculum of
math courses in high school. Suppose a random sample of 200 students who completed
this core set of courses results in a mean math score of 20.6 on the college entrance
exam with a standard deviation of 3.6.
.
Do these results suggest that students who complete the core curriculum are ready for
college-level mathematics? Thatis, are they scoring above 20 on the math portion of the
exam? Complete parts a through d below.
Statcrunch solution: Go to stat--T-Stat-One Sample Data Summary.
Sample mean put 20.6
Sample std. dev. put 3.6
Sample size put 200
H0: m= 20
HA:m> 20
b) Verify that the requirements to perform the test using thet-distribution are satisfied. Is
the sample obtained using simple random sampling or from a randomizedexperiment?
Yes because the students were randomly sampled.
Is the population from which the sample is drawn normally distributed or is the sample
size, n, large (n> or =30)
, Yes, the sample size is larger than 30.
Are the sample values independent of each other?
Yes, because each student's test score does not affect the other student's test scores.
c) P-value =0.009 from your statcrunch
State the conclusion for the test. Reject the null hypothesis because the P-value is less
than the a=0.10 level of significance.
We have an expert-written solution to this problem!
Statcrunch solution: For Test Statistic T0
Go to stat--T-Stat-One Sample Data Summary.
Sample mean put 8.37
Sample std. dev. put 0..7
Sample size put 12
H0: m= 9.02
HA:m> 9.02
Compute: T0=-3.22
Statcrunch solution for P-value: Go to stat-calculators-T calculator.
DF=12
P(X<-3.22
Calculate
P value is 0.004
What conclusion can bedrawn?
Reject H0: There is sufficient evidence to conclude that the hippocampal volumes in the
alcoholic adolescents are less than the normal volume of 9.02 cm3
#3 Question open picture
#4 A health administration recommends that individuals consume 950 mg of calcium
daily. After an advertising campaign aimed at maleteenagers, a dairy association states
that male teenagers consume more than the recommended daily amount of calcium. To
support thisstatement, the association obtained a random sample of 40 male teenagers
and found that the mean amount of calcium consumed was 960mg, with a standard
deviation of 100 mg. Is there significant evidence to support the statement of the
association at the alpha equals 0.05 level ofsignificance?
For statcrunch solution open picture
What conclusion can be drawn?
#1 Several yearsago, the mean height of women 20 years of age or older was 63.7
inches. Suppose that a random sample of 45 women who are 20 years of age or older
today results in a mean height of 64.4 inches.
(a) State the appropriate null and alternative hypotheses to assess whether women are
taller today.
(b) Suppose theP-value for this test is 0.02 Explain what this value represents.
(c) Write a conclusion for this hypothesis test assuming an alpha=0.10 level of
significance.
For answers for a) and b) open picture
d)
(c) Write a conclusion for this hypothesis test assuming a=0.10 level of significance.
Reject the null hypothesis. There is sufficient evidence to conclude that the mean height
of women 20 years of age or older is greater today
#2 A college entrance exam company determined that a score of 20 on the mathematics
portion of the exam suggests that a student is ready forcollege-level mathematics. To
achieve thisgoal, the company recommends that students take a core curriculum of
math courses in high school. Suppose a random sample of 200 students who completed
this core set of courses results in a mean math score of 20.6 on the college entrance
exam with a standard deviation of 3.6.
.
Do these results suggest that students who complete the core curriculum are ready for
college-level mathematics? Thatis, are they scoring above 20 on the math portion of the
exam? Complete parts a through d below.
Statcrunch solution: Go to stat--T-Stat-One Sample Data Summary.
Sample mean put 20.6
Sample std. dev. put 3.6
Sample size put 200
H0: m= 20
HA:m> 20
b) Verify that the requirements to perform the test using thet-distribution are satisfied. Is
the sample obtained using simple random sampling or from a randomizedexperiment?
Yes because the students were randomly sampled.
Is the population from which the sample is drawn normally distributed or is the sample
size, n, large (n> or =30)
, Yes, the sample size is larger than 30.
Are the sample values independent of each other?
Yes, because each student's test score does not affect the other student's test scores.
c) P-value =0.009 from your statcrunch
State the conclusion for the test. Reject the null hypothesis because the P-value is less
than the a=0.10 level of significance.
We have an expert-written solution to this problem!
Statcrunch solution: For Test Statistic T0
Go to stat--T-Stat-One Sample Data Summary.
Sample mean put 8.37
Sample std. dev. put 0..7
Sample size put 12
H0: m= 9.02
HA:m> 9.02
Compute: T0=-3.22
Statcrunch solution for P-value: Go to stat-calculators-T calculator.
DF=12
P(X<-3.22
Calculate
P value is 0.004
What conclusion can bedrawn?
Reject H0: There is sufficient evidence to conclude that the hippocampal volumes in the
alcoholic adolescents are less than the normal volume of 9.02 cm3
#3 Question open picture
#4 A health administration recommends that individuals consume 950 mg of calcium
daily. After an advertising campaign aimed at maleteenagers, a dairy association states
that male teenagers consume more than the recommended daily amount of calcium. To
support thisstatement, the association obtained a random sample of 40 male teenagers
and found that the mean amount of calcium consumed was 960mg, with a standard
deviation of 100 mg. Is there significant evidence to support the statement of the
association at the alpha equals 0.05 level ofsignificance?
For statcrunch solution open picture
What conclusion can be drawn?
