Practice set 3 | Mathematics homework help


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Practice Set 3


Practice Set 3



1.   Let x be a continuous random variable. What is the probability that x assumes a single value, such as a (use numerical value)?


2. Thefollowingarethethreemaincharacteristicsofanormaldistribution.

A.    Thetotalareaunderanormalcurveequals _____.

B.    Anormalcurveis___________aboutthemean.Consequently,50%ofthetotalareaunderanormaldistributioncurveliesontheleftsideofthe mean,and50%liesontherightsideofthemean.

C.    Fill in the blank. Thetailsofanormaldistributioncurveextendindefinitelyinbothdirectionswithouttouchingorcrossingthehorizontalaxis.Althoughanormalcurvenevermeetsthe________axis,beyondthe pointsrepresentedby µ   to µ+ 3σ itbecomessoclosetothisaxisthattheareaunderthecurve beyondthesepointsinbothdirectionsisveryclosetozero.

3. For the standard normal distribution, find the area within one standard deviation of the  

          mean that is, the area between μ − σ and μ + σ. Round to four decimal places.


4. Find the area under the standard normal curve. Round to four decimal places.

a)     between z = 0 and z = 1.95

b)    between z = 0 and z = −2.05

c)     between z = 1.15 and z = 2.37

d)    from z = −1.53 to z = −2.88

e)     from z = −1.67 to z = 2.24


5.     Theprobabilitydistributionofthepopulationdataiscalledthe (1) ________.Table7.2inthe textprovidesanexampleofit.Theprobabilitydistributionofasamplestatisticiscalledits (2) _________.Table7.5inthetextprovidesanexampleit.

A.    Probability distribution

B.    Population distribution

C.    Normal distribution

D.    Sampling distribution


6. ___________isthedifferencebetweenthevalueofthesamplestatisticandthevalueofthecorrespondingpopulationparameter,assumingthatthesampleisrandomandnonon-samplingerrorhasbeenmade.Example7–1inthetextdisplayssamplingerror.Samplingerroroccursonlyinsamplesurveys.


7. Consider the following population of 10 numbers. 20 25 13 19 9 15 11 7 17 30

a)     Find the population mean. Round to two decimal places.

b)    Rich selected one sample of nine numbers from this population. The sample included the numbers 20, 25, 13, 9, 15, 11, 7, 17, and 30. Calculate sampling error for this sample. Round to decimal places.


8. Fill in the blank. TheFdistributionis________andskewedtotheright.TheFdistributionhastwo numbersofdegreesoffreedom:dfforthenumeratoranddfforthedenominator.TheunitsofanFdistribution,denotedbyF,arenonnegative.


9. Find the critical value of F for the following. Round to two decimal places.

a)     df = (3, 3) and area in the right tail = .05

b)    df = (3, 10) and area in the right tail = .05

c)     df = (3, 30) and area in the right tail = .05


10. The following ANOVA table, based on information obtained for three samples selected from three independent populations that are normally distributed with equal variances, has a few missing values.

Source of


Degrees of


Sum of




Value of the

Test Statistic










F = ___V__ = VII








a)     Find the missing values and complete the ANOVA table. Round to four decimal places.

b)    Using α = .01, what is your conclusion for the test with the null hypothesis that the means of the three populations are all equal against the alternative hypothesis that the means of the three populations are not all equal?

  1. Reject H0. Conclude that the means of the three populations are equal.
  2. Reject H0. Conclude that the means of the three populations are not equal.
  3. Do not reject H0. Conclude that the means of the three populations are equal.
  4. Do not reject H0. Conclude that the means are of the three populations are not equal.



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