QNT/275 Week 3 Practice Set problems

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.Althoughanormal curvenevermeetsthe________ axis,beyondthepointsrepresentedby µ -3? to µ+3?itbecomessoclosetothisaxisthattheareaunderthecurve beyondthesepointsinbothdirectionsisveryclosetozero.

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

mean that is, the area between ? ? ? and ? + ?.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)________.Table7.2inthetextprovidesanexample ofit.Theprobabilitydistributionofasamplestatistic iscalledits (2) _________.Table7.5inthetextprovides anexampleit.

A. Probability distribution

B. Population distribution

C. Normal distribution

D. Sampling distribution

6. ___________isthedifferencebetween thevalueofthesamplestatistic andthevalueofthecorrespondingpopulationparameter,assumingthatthesampleisrandom andnonon-samplingerror hasbeenmade.Example 7–1inthetextdisplayssamplingerror. Samplingerroroccurs onlyinsamplesurveys.

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:dfforthenumerator anddfforthedenominator.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 Variation	Degrees of Freedom	Sum of Squares	Mean Square	Value of the Test Statistic
Between	2	II	19.2813
Within		89.3677	III	F = ___V__ = VII VI
Total	12	IV

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

b) Using ? = .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.