Instruction

Workout the following problems and show all necessary steps to earn full credit.

1.In a random sample of 40 refrigerators, the mean repair cost was $150.Assumethe population standard deviation =$15.5.

a.Construct a 99% confidence interval for the population mean repair cost.Interpret the interval in the context of the problem.[Use Algebra first then Tech next](4points)

b.Repeat exercise 1(a), changing the sample size to n = 60. Which confidence interval has better estimate?Why?Explain?[Use Algebra first then Tech next](3points)

c.Repeat exercise 1(a), using a population standard deviation of = $19.5. Which confidence interval iswider?Explain?[Use Algebra first then Tech next](3points)

2.The SAT scores of 12 randomly selected high school seniors are givenas:

1700

1940

1510

2000

14301870

1990

1650

1820

1670

22101380

Assume the population distribution is normal and the population standard deviation() is UNKNOWN.

a.Find thesamplemean[usetechnology](2points)

b.Find the sample standard deviation[usetechnology](2points)

c.Constructa99%confidenceintervalforthepopulationmean.(3points)

d.Construct a 95% confidence interval for the population mean .Interpretthe interval in the context of the problem.

(4 points)

e.How does decreasing the level of confidence in part (d) change the width of theconfidenceinterval?Explain?(3points)

3.Inarandomsampleof50 people,themeanbody massindex(BMI)was27.7 andthe sample standard deviation (s) was6.12.The population standard deviation() is UNKNOWN.

a.Constructa90%Confidenceintervalforthepopulationmean.(3points)

[Use Algebra first then Tech next]

b.Constructa96%Confidenceintervalforthepopulationmean.(3points)

[Use Algebra first then Tech next]

4.Inasurveyof2383U.S.adults,1073thinkthatthereshouldbemoregovernmentregulation of oilcompanies.

a.Find the point estimate for the population proportion P of U.S. adults who think that there should be more government regulation ofoilcompanies.(2points)

b.Construct a 95% confidence interval for the population proportion.Interpretthe results.[Use Algebra first then Tech next]

(4points)

c.Findtheminimumsamplesizeneededtoestimatethepopulationproportionatthe99% confidence level in order to ensure that the estimate is accurate within 3% of the populationproportion.N. B. Use the point estimate from part 4(a).(4points)

[Use Algebra first then Tech next]

5.TheGeneticsandIVFInstituteconductedaclinical trialoftheYSORTmethoddesignedtoincreasetheprobabilityofconceivingaboy.Asofthiswriting,291babieswereborntoparentsusing theYSORTmethod,and 239ofthem wereboys.UsesignificanceleveltotesttheclaimthattheYSORT methodiseffectiveinincreasingthelikelihood thatababywillbeaboy.[Use Algebra first then Tech next]

a.Statethenullandalternatehypotheses(writeitmathematically)andwriteyourclaim.

(2points)

b.Find theteststatistic.(3points)

c.Identify the Rejection region (critical region) and fail to reject region. Show this by drawing a curve and separate the rejection region from the fail to reject region using the critical value.(3points)

d.Find thep-value and interpret its meaning.(2points)

e.Decidewhethertorejectorfail torejectthenull usingthep-valueapproach.

(2points)

f.Makeaninterpretationofyourdecisionin thecontextoftheclaim.(2points)

g.What is Type 1 error in this problem? Explain its consequence in the context of the problem.(2points)

h.Use the sample data to construct a 90% confidence interval estimate of the proportion of boys (. What does the confidence interval suggest about the claim thattheYSORT methodiseffectiveinincreasingthelikelihood thatababywillbeaboy ()?[Use Tech](3points)

6)Amedicalresearcherclaimsthatlessthan 24%ofadultsin acertain countryaresmokers.Inarandomsampleof250adultsfromthatcountry,18%saythattheyaresmokers. At significance level of,isthereenough evidencetosupporttheresearcher'sclaim?

[Use Algebra first then Tech next]

a.Statethenullandalternatehypotheses(writeitmathematically)andwriteyourclaim.(2points)

b.Find theteststatistic.(3points)

c.Identify the Rejection region (critical region) and fail to reject region. Show this by drawing a curve and separate the rejection region from the fail to reject region using the critical value.

(3points)

d.Find thep-value andinterpret its meaning.(2points)

e.Decidewhethertorejectorfail torejectthenull usingthep-valueapproach.(2points)

f.Makeaninterpretationofyourdecisionin thecontextoftheclaim.(2points)

7)The results of a state mathematics test for random samples of students taught by two different teachers at the same school are shown below. Can you conclude there is a differenceinthemeanmathematicstestscoresforthestudentsofthetwoteachers?Use(alpha) = 0.01

In addition, assume the populations are normally distributed and the populationvariances/standard deviations are UNKNOWN and NOT EQUAL.

Teacher 1

Teacher 2

1=473

2=459

S₁= 39.7

S₂= 24.5

n₁= 8

n₂= 18

a.State the null and alternate hypotheses (write it mathematically) andwrite yourclaim.

(2 Points)

b.Find the teststatistic(3 Points)

[Use Algebra first then Tech next]

c.Identify the Rejection region (critical region) and fail to reject region. Show this by drawing a curve and separate the rejection region from the fail to reject region using the critical values.(3 Points)

d.Decide whether to reject or fail toreject thenull.( 2points)

e.Make an interpretation of your decision inthecontext.( 2points)

8)Considerthefollowingdataofthenumberofhours12studentsspentonlineduring the weekend and the scores of each student who took a test thefollowing Monday.

Hrsspent

online(x)

0

1

2

3

3

5

5

5

6

7

7

10

Testscores(y)

96

85

82

74

95

68

76

84

58

65

75

50

a.Find the sample linear correlation coefficient andinterpretit.( 3points)[Use Tech]

b.Is the population correlation coefficient significant/ is there a significant linear correlation?[ use=0.01](2points)

c.Find the equation of the regression line. What is theslope of the line?Interpret this value inthecontext?( 4points)

d.What is the coefficient of determination?Interprettheresult?( 2points)

e.Ifwere 3 hours, what would you expecttobe?( 2points)

f.Ifwere 6 hours, what would you expecttobe?( 2points)

g.Ifwere 25 hours, what would you expecttobe?( 2points)

9)AccordingtotheCensusBureau,thedistributionbyethnicbackgroundoftheNew York City population in a recent yearwas

Hispanic:28%Black:24%White:35%Asian:12%Others:1%

The manager of a large housing complex in the city wonders whether the distribution by race of the complex's residents is consistent with the population distribution. To find out, she records data from random sample of 800 residents. The table below displays the sample data.

Race

Hispanic

Black

White

Asian

Others

Count

212

202

270

94

22

Are these data significantly different from the city's distribution by race? Carry out an appropriate test at the = 0.05level of significance to support your answer.

[Use Algebra first then Tech next]

a.State the null and alternate hypotheses (write it mathematically) andwrite yourclaim.

(2Points)

b.Find theteststatistics.(3Points)

c.Identify the Rejection region (critical region) and fail to reject region. Show this by drawing a curve and separate the rejection region from the fail to reject region using the critical value.

(3 Points)

d.Decide whether to reject or fail toreject thenull.( 2Points)

e.Make aninterpretation of your decision inthecontext.( 2Points)

10)Isachievingabasicskilllevelrelatedtothelocationoftheschool?Theresultsofa random sample of students by the location of school and the number of students achieving basic skill level in three subjects is shown in the contingency table. At = 0.05, answer thefollowing:

Subject

Location

Reading

Math

Science

Urban

40

49

41

Suburban

60

66

68

[The two categorical variables here areSubjectandLocationwithtwoandthree

Categories respectively][Use Algebra first then Tech next]

a.State the null and alternate hypotheses (write it mathematically) andwrite yourclaim.

(2points)

b.Find the standardizedteststatistic( 3Points)

c.Decide whether to reject or fail toreject thenull.( 2Points)

d.Make an interpretation of your decision inthecontext.( 2Points)