TRUE OR FALSE+Solution

TRUE OR FALSE
2. You cannot make a Type I error when the null hypothesis is true. (Ch9)

3. For a continuous distribution, the exact probability of a particular value is always

5. For a continuous distribution, Probability of (X greater than or equal to 10) is less than the probability of (X greater than 10) (Ch6)
7. We do not need to perform the continuity correction if the population is 20 times or more than the sample size.(Ch6)

8. For a binomial probability experiment, with n=150 and p=.1, we can use the normal approximation to the binomial distribution even without continuity correction. (Ch6)

12. In a regression model the population of potential error terms is assumed to have a t-distribution. (Ch13)

13. If the population is normally distributed with known variance then the sample mean may not be normally distributed for very small sample size.
14. When constructing a confidence interval for a sample proportion, the t distribution is always appropriate if the sample size is small. (Ch8)

16. An estimator is called consistent if its variance and standard deviations consistently remain the same regardless of changes in the sample size.(Ch7)

17. The level of significance indicates the probability of rejecting a false null hypothesis.

19. When the population is normally distributed and the population standard deviation  is unknown, then for any sample size n, it is appropriate to build the confidence interval of Xbar based on the t distribution.

MULTIPLE CHOICE

21. If we are testing the significance of the independent variable X1 in Regression and we reject the null hypothesis H0: 1=0, we conclude that: (Ch13)

X1 is significantly related to Y
X1 is not significantly related to Y
X1 is an unimportant independent variable
1 is significantly related to the dependent variable Y

22. For a given multiple regression model with three independent variables, the value of the adjusted multiple coefficient of determination is _________ less than R2.
Always
Sometimes
Never
Can be greater or less depending on the standard error

27. When we carry out a chi-square test of independence, as the difference between the respective observed and expected frequencies decrease, the probability of concluding that the row variable is independent of the column variable:
Decreases
Increases
May increase or decrease depending on the number of rows and columns

Will be unaffected
29. As standard deviation increases, samples size _____________ to achieve a specified level of confidence.
Increases
Decreases
Remains the same

Sometimes increases and sometimes decreases

3. The MPG (Miles per Gallon) for a mid-size car is normally distributed with a mean of 32 and a standard deviation of .8. What is the probability that the MPG for a selected mid-size car would be: More than 33.2? 43.32%
6.68%
93.32%
86.64%
13.36%

34. A state education agency designs and administers high school proficiency exams. Historically, time to complete the exam was an average of two hours with a standard deviation of 5 minutes. Recently the format of the exam changed and the claim has been made that the time to complete the exam has changed. A sample of 50 new exam times yielded an average time of 118 minutes. Calculate a 99% confidence interval based on the sample result.
[117.61 120.09]
[117.36 119.39]
[116.18 119.82]
[115.67 120.33]
[115.82 120.18]

ESSAY QUESTIONS

35.
At a recent meeting of educational researchers comparison were made between the type of college freshmen attend and the numbers who drop out. A random sample of freshmen show the following results: (keep two decimals in calculating expected frequencies)
4Yr public 4Yr private 2Yr public 2Yr private
drop out 10 9 15 9
don’t drop 26 28 18 27
Use a significance level of .05 and determine if the type of school and the drop out rate are independent. (Ch12)
(Points : 20)

36. In an opinion survey, a random sample of 1000 adults from the U.S.A and 1000 adults from Germany were asked whether they supported the death penalty. 590 American adults and 560 German adults indicated that they supported the death penalty. The researcher wants to know if there is sufficient evidence to conclude that the proportion of adults who support the death penalty is higher in the U.S.A. than in Germany. What is the decision at a =.05 and 0.10 (Ch10)
(Points : 20)

37. An apple juice producer buys all his apples from a conglomerate of apple growers in one northwest state. The amount of juice squeezed from each of these apples is known to be normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce.
Between what two values (in ounces) symmetrically distributed around the population mean will 80% of the apples fall? (Ch6) (Points : 20)

38.
A small town has a population of 15,000 people. Among these 1,500 regularly visit a popular local bar. A sample of 225 people from those who regularly visit the bar is surveyed for their annual expenditures in the bar. It is found that on average each person who regularly visits the bar spends about $2000 per year in the bar with a standard deviation of $196. Construct a 99 percent confidence interval around the mean annual expenditure in the bar. (Ch7 and 8)
(Points : 20)

39.
Historically the average age of European soccer players is reported as 26 years with a standard deviation of 4 years and is assumed to be normally distributed. A random sample of 81 European professional soccer players has an average age of 27 years. We would like to decide if there is enough evidence to establish that average age of European soccer players has increased significantly. What is the decision at =.05 and 0.01? Indicate which test you are performing; show the hypotheses, the test statistic and the critical values and mention whether one-tailed or two-tailed. (Ch9)
(Points : 20)

40. A human resource manager is interested in whether absences occur during the week with equal frequency. The manager took a random sample of 100 absences and created the following table:
Monday 28
Tuesday 20
Wednesday 12
Thursday 18
Friday 22

At a significance level of alpha = .05 test the Null that the probabilities of absences are the same for all five days. (Ch12)

(Points : 20)

41. The weight of a product is normally distributed with a standard deviation of .5 ounces. What should the average weight be if the production manager wants no more than 10% of the products to weigh more than 4.8 ounces? (Ch6) (Points : 20)

42. A set of final examination grades in a calculus course was found to be normally distributed with a mean of 69 and a standard deviation of 8.
Only 5% of the students taking the test scored higher than what grade? (Ch6)
(Points : 20)

43.
Test H0: pi1– pi2 .01, HA: pi1– pi2 > .01 at  =.05 where p1=.08, p2=.035, n1 = 200, n2 = 400. Indicate which test you are performing; show the test statistic and the critical values and mention whether one-tailed or two-tailed.
Note that pi stands for the Greek letter representing population proportion. (Ch10)
(Points : 20)

44. Consider the following partial computer output for a multiple regression model.
Predictor Coefficient Standard Deviation

Constant 41.225 6.380
X1 1.081 1.353
X2 -18.404 4.547

Analysis of Variance
Source DF SS
Regression 2 2270.11
Error 26 3585.75
What is the number of Observations in the sample? Write the least squares regression (prediction) equation. Test the usefulness of variable x2 in the model at alpha =.05. Calculate the t statistic and state your conclusions. (Ch14)
(Points : 20)