# Project #23181 - statistics

1. A samplin method is -------------------when the individuals selected for one sample are used to determine the individuals in the second sample.

2. Determine whether the following sampling is independent or independent.

A. The sampling is dependent because an individual selected for one sample does not dictate which individuals is to be in the second sample.

B. The sampling is independent because an individual selected for one sample does not dictate which individual is to be in the second sample.

C. The sampling is dependent because an individual selected for one sample does dictate which individual is to be in the second sample.

D. The sampling is independent because an individual selected for one sample does dictate which individuals is to be in the second sample.

Indicate whether the response variable is qualitative or quantitative

A.      The variable is qualitative because it is an attribute classification.

B.      The variable is qualitative because it is a numerical measure

C.      The value is quantitative because it is a numerical measure

D.      The variable is quantitative because it is an attribute classification

Suppose there are n independent trials of an experiment with k >3 mutually exclusive outcomes, where pi represents the probability of observing the ith outcome. What would be the formula of an expected count in this situation?

A.      The expected counts for each possible outcome are given by E1=n/pi.

B.      The expected counts for each possible outcome are given by Ei=n

C.      The expected counts for each possible outcome are given by Ei=npi

D.      The expected counts for each possible outcome re given by Ei=pi.

4. The expected frequencies in a chi-square test for independence are found using the formula:

Expected frequency = (row total)(column total)/table total

A.      False. The expected frequencies for all chi-square test are given by Oi-Ei/Ei, where I represents cell number.

B.      True. It is a simplification of multiplying the proportion of a row variable by the proportion of the column variable to find the proportion for a cell, then multiplying by the table total.

C.      True. The area to the right of this value in the corresponding chi-square distribution given the p-value for the test.

D.      False. This formula gives the expected proportion. The (table) total factor in the denominator on the right should be squared.

5. An economist wants to determine whether the region a resident lives is associated with education. He randomly selects 1558 residents and obtains the following data. Complete parts a and b.

East                  56                                104                     118                   98

North               66                                  121                     127                   103

South                80                                  122                      85                    112

West                  59                                   112                     102                  93

Significance.

A.      Reject Ho. There is sufficient evidence that education and region are associated.

B.      Fail to reject Ho. There is sufficient evidence that education and region are associated.

C.      Fail to reject Ho. There is not sufficient evidence that education and region are associated.

D.      Reject Ho. There is not sufficient evidence that education and region are associated.

b. Construct a conditional distribution by region and draw a bar graph.

East          ____                                 ____             ___                      _____

North       ____                                 ____              ___                     ____

South       ____                                 ____              ___                      ___

West        ____                                  ____             ___                       ____

(round to three decimal places as needed)

6. A survey of 36 randomly selected students who dropped a course was conducted at a college. The following results were collected

F  Work        M  Course  M  Work

F  personal  M  Work    F   Personal

F  work         M  work    M  Personal

M Personal  F Course   F course

M work        M Course   M work

M Personal   F  Personal  M course

M course      F  work         M course

M Personal  M work          F personal

F personal     F course     M work

M Course    F work         M personal

F work        M work       F personal

F personal   M personal  F personal

a.       Construct a contingency table for the two variables.

Course    Personal     Work

Male             ___            ___            __

Female          ___            ___          ___

b.      Is gender independent of drop reason at the a=0.1 level of significance?

A.      Reject Ho. There is not sufficient evidence that gender and drop reason are dependent.

B.      Fail to reject Ho. There is sufficient evidence that gender and drop reason are dependent.

C.      Reject Ho. There is sufficient evidence that gender and drop reason are dependent.

D.      Fail to reject Ho. There is not sufficient evidence that gender and drop reason are dependent.

c) Construct a conditional distribution of drop reason by gender and draw a bar graph.

Course       Personal     Work

Male          __                     __            __

Female      __                     __            __

Total       1                           1                 1

(round to three decimal places as needed)

7. To perform a one-way NOVA , the population do not need to be normally distributed.

A. True    B. False

8. To perform a one-way NOVA, the populations must have the same variance

A. True   B. False

9. The variability among the sample mean is called _______(between-sample variability, the mean square error, within sample variability, the f-test statistic) and the variability of each sample is the _____(between-sample variability, the mean square error, within sample variability, the f-test statistic)

10. Determine the F-test statistic based on the given summary statistics.

Population    Sample size    Sample mean    Sample variance

1                        10                     34                        24

2                        10                      47                        43

3                        10                      45                         28

F=____(round to two decimal places as needed)

11. Is the one-way NOVA test robust?

A. Yes, small departures from the normality requirement do not significantly affect the results

B. Yes, outliers in the data do not significantly affect the results

C. No, outliers in the data significantly affect the results

D. No, small departures from the normality requirement significantly affect the results.

12. A researcher wants to show the mean from population is less than the mean from population 2 in matched-pairs data. If the observations from sample 1 are Xi, and the observations from sample 2 are Yi, and di, =Xi-Yi, then the null hypothesis is Ho: Uc= 0 and the alternative hypothesis is H1:Uc____( <, >, <, >, and equal sign with a dash on it)

-   -

13. Some people believe that higher-octane fuels result in better gas mileage for their car. To test this claim, a researcher randomly selected 11 individuals (and their cars) to participate in the study. Each participant received 10 gallons of gas and drove his car on a closed course. The number of miles driven until the car ran out of gas was recorded. A coin flip was used to determine whether the car was filled up with 87-octane or 92-octane first, and the driver did not know which fuel was in the tank.

87-octane 234  258  242    216    115  288  316  230  192  205  547

92-octane 237  237  228    224    119  296  350  240   186  208  562

a.       Why is it important that the matching be done by driver and car?

A.      So that each driver can determine which fuel is best for their car

B.      So that all the trials can be done at the same time

C.      Cuts the cost of doing research

D.      How someone drives and the car they drive result in different fuel consumption

b.      Why is it important to conduct the study on a closed track?

A.      So that all drivers and cars have similar driving conditions

B.      So that the researcher can watch the drivers

C.      So that each car travels the same distance

c.       Are either of these variables normally distributed?

A.      Yes, both variables are normally distributed

B.      Yes, 87-octane is normally distributed

C.      No, either variable is normally distributed

D.      Yes, 92-octane is normally distributed

d.      The researchers used a statistical software package to determine whether the mileage from 92-octane is greater than the mileage from 87-octane. The results are given below.

Paired T –test and CI: 92 octane, 87 octane

Paired t for 92 octane -87 octane

N     Mean       StDEV       SE Mean

92 octane   11   258.455     108.985    32.860

87 octane    11    262.455     115.053   34.690

Difference  11      4.000         14.629      4.411

T-Test of mean difference =0 (vs>0): T-Value=0.91 P-Value =0.193

What do you conclude at a=0.05? why?

A.      Fail to reject the null hypothesis because P-value is greater than 0.05

B.      Fail to reject the null hypothesis because P-value is less than 0.05

C.      Reject the null hypothesis because the P-value is greater than 0.05

D.      Reject the null hypothesis because the P- value is less than 0.05

14. A study was conducted to determine the effectiveness of a certain treatment. A group of 102 patients were randomly divided into an experimental group and a control group. The table shows their result for their net improvement. Let the experimental group be group 1 and the control group be group 2.

Experimental                 Group

n                       61                                    41

_

X                         11.2                                3.4

S                           6.4                                   6.6

a.       Test whether the experimental group experienced a larger mean improvement than the control group at the a=0.01 level of significance.

Should the null hypothesis be rejected.

A.      No, because the test statistic is not in the critical region

B.      Yes, because the test statistic is not in the critical region

C.      No, because the test statistic is in the critical region

D.      Yes, because the test statistic is in the critical region

b.      Construct a 95% confidence interval about u1-u2 and interpret the results .4

Therefore, the confidence interval is the range from ___to___ (round to two decimal places as needed)

What is the interpretation of this confidence interval?

A.      There is 95% probability that the difference of the means is interval

B.      There is 95% probability that the difference between randomly selected individuals will be in the interval

C.      We are 95% confident that the difference of the means is in the interval

D.      We are 95% confident that the difference between randomly selected individuals  will be in the interval

15. A random sample of 40 adults with no children under the age of 18 years results in a mean daily leisure time of 5.26 hours, with a standard deviation of 2.48 hours. A random sample of 40 adults with children under the age of 18 results in a mean daily leisure time of 4.32 hours, with a standard deviation of 1.52 hours. Construct and interpret a 90% confidence interval for the mean difference  in leisure time between adults with no children and adults with children (U1-U2)

Let U1 represent the mean leisure hours of adults with no children under the age of 18 and U2 represents the mean leisure hours of adults with children under the age of 18.

The 90%  confidence interval for (U1-U2) is the range from ____to___hours

(round to two decimal places)

What is the interpretation of this confidence interval?

A.      There is 90% probability that the difference of the means is in the interval. Conclude that there is insufficient evidence of a significant difference in the number of leisure hours.

B.      There is 90% confidence that the difference of the means is in the interval. Conclude that there is a significant difference in the number of leisure hours.

C.      There is a 90% confidence that the difference of the means is in the interval. Conclude that there is insufficient evidence of a significance difference in the number of leisure hours.

D.      There is 90% probability that the difference of the means is in the interval. Conclude that there is significant difference in the number of leisure hours.

16. Discussion
The heights and weights of 11 men between the ages of 21 and 26 were measured.
The data are presented in the table below.

 Height (Inches), x 75 66 71 67 70 72 72 70 72 76 69 Weight (Pounds), y 187 151 183 155 179 175 181 173 194 212 160

1.         Draw and interpret a scatter diagram of the data, treating the height as the explanatory variable.

2.         Compute and interpret the linear correlation coefficient between the height and the weight of the men in the sample.

3.         Comment on the type of relation that appears to exist between the height and the weight of the men based on the scatter diagram and the linear correlation coefficient.

4.         Explain the difference between correlation and causation.

 Subject Mathematics Due By (Pacific Time) 02/19/2014 11:00 am
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