Practice Set 3

 

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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. Thefollowing arethethree maincharacteristics of anormal distribution.

A.    Thetotal areaunder anormal curve equals _____ .

B.    Anormal curve is ___________ aboutthe mean. Consequently,50%ofthe total areaunder anormal distribution curve liesontheleftside ofthe mean, and50%lies ontheright side ofthemean.

C.    Fill in the blank. Thetails ofanormal distributioncurve extend indefinitely in bothdirections without touching orcrossing the horizontal axis. Although anormal curve never meets the________ axis, beyondthe points represented by µ – 3σ    to µ+ 3 σ it becomesso close to this axisthatthe areaunderthe curve beyond these pointsin bothdirections is veryclose to zero.

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.     Theprobability distribution of the population datais called the (1) ________. Table7.2in the text providesanexample of it. Theprobability distribution of asample statistic is calledits (2) _________. Table7.5in the text providesanexample it .

A.    Probability distribution

B.    Population distribution

C.    Normal distribution

D.    Sampling distribution

 

6. ___________ is thedifference betweenthevalue ofthesample statistic andthe value of the corresponding population parameter, assuming thatthesample is randomand no non-sampling errorhas beenmade. Example 7–1in thetext displays sampling error.Sampling erroroccurs onlyin sample surveys.

 

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. TheFdistribution is ________and skewed to the right. TheFdistribution has two numbersofdegrees of freedom: dffor the numerator and dffor the denominator. Theunits ofan Fdistribution, denoted byF,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

VariationDegrees of

FreedomSum of

SquaresMean

SquareValue of the

Test Statistic

Between

2

II

19.2813

 

Within 

89.3677

IIIF = ___V __ = VII

VI

Total

12

IV

 

 

 

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?Reject H0. Conclude that the means of the three populations are equal.Reject H0. Conclude that the means of the three populations are not equal.Do not reject H0. Conclude that the means of the three populations are equal.Do not reject H0. Conclude that the means are of the three populations are not equal.

 

 

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