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There are 51 questions ...MORE
Subject: Mathematics | Topic: Statistics | ID: 155697
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100 particles, contained in a box with a separating wall. If the separating wall is removed and the particles can move freely, what is the probability that
a) There are 50 particles in each half?
b) There are 100 particles in one half?
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Subject: Mathematics | Topic: Statistics | ID: 157703
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100 particles, contained in a box with a separating wall.
If the separating wall is removed and the particles can move freely,
calculate the entropic difference (based on 1 mol) ...MORE
Subject: Mathematics | Topic: Statistics | ID: 157704
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A 5 mol He-bubble is in water, the waters T increases by 20, but the bubbles volume remains constant.
We assume that it is an ideal and mono-atomic helium bubble.
Calculate the energy U ...MORE
Subject: Mathematics | Topic: Statistics | ID: 157705
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$ 2.0 |
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1) “µ = 17” is an appropriate null hypothesis.
A. True
B. False
2) The value that separates a rejection region from a non-rejection region is called the test statistic.
A. True
B. False
3) If the p-value is less than Alfa in a two-tailed test, the null should be rejected.
A. True
B. False
4) A statistician was setting up a hypothesis test with a level of significance dictated by upper management. However, she was concerned that the test she wished to perform might have unacceptable large possibilities of Type II error, Beta. Which of the following would solve this problem?
A. Convince upper management to reduce the level of significance of the test
B. Convince upper management to use a larger sample.
C. Convince upper management to use a larger p-value.
D. Convince upper management to use a smaller p-value.
5) We have created a 95% confidence interval for µ with the result [10, 15]. What conclusion will we make if we test H_0: Mu = 16 versus H1: Mu ? 16 at alfa = 0.05?
A. We cannot tell what our decisions will be from the information
B. Fail to reject the null.
C. Accept the null.
D. Reject the null and conclude the alternative.
6) The Roman Senate has become concerned about the loyalty of the army in Gaul commanded by Julius Caesar. They claim that, of the 80,000 men in the army, at least 28,000 are foreign barbarians. Caesar believes there are fewer barbarians, so the Senate should not worry. He polls one legion of 1,000 men and finds that 340 of them are barbarians. What is the test statistic for this hypothesis test?
A. (0.34-0.35)/0.063
B. (0.34-0.35)/0.015
C. (0.35-0.34)/100
D. (0.35-0.34)/0.2275
7) When testing for differences between two means, the Behrens-Fisher problem arises when the sample populations are
A. are non-normal and have unequal variances.
B. are normal with unequal variances.
C. normal with equal variances.
D. are non-normal and have equal variances.
8) A test for equality of two variances has samples sizes n1 = 13 and n2 = 10. The degrees of freedom for the test are
A. 12 and 9.
B. 26 .
C. 21 .
D. 13 and 10.
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Subject: Mathematics | Topic: Statistics | ID: 158556
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$ 5.0 |
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9) Degrees of freedom for a test of mean differences with unequal variances is
A. n - 2
B. n1 + n2 – 1
C. n - 1
D. n1 + n2 - 2
10) In a test of the equality of two means, the variable of interest is the difference between the values of the observations, rather than the observations.
A. True
B. False
11) In a test for the equality of two variances (two-tailed), when the populations are normal, a 5% level of significance was used. Sample sizes were n1 = 13 and n2 = 10. The upper critical value for the test is
A. = FINV(1-0.025, 13, 10).
B. = FINV(0.05, 12, 9).
C. = FINV(0.025, 13, 10). .
D. = FINV(0.025, 12, 9).
12) Which of the following statements is false for an F-distribution?
A. Degrees of freedom for the numerator may be larger, smaller, or equal to the degrees of freedom for the denominator.
B. Variables that are F distributed range from 0 to infinity.
C. Degrees of freedom for the denominator are always smaller than degrees of freedom for the numerator.
D. The exact shape of the distribution is determined by two numbers of degrees of freedom.
13) The use of the Student’s t distribution requires which of the following assumptions?
A. The sample is drawn from a positively skewed distribution.
B. The sample size is greater than 30.
C. The population is normal.
D. The population variance is known.
14) The expected value of the sampling distribution of the sample mean equals the populations mean
A. For all populations.
B. When the population is normally distributed
C. When the population size N>30.
D. When the population is symmetric.
15) The standard error of the sample mean is equal to 5 when n=25. If the sample size increases by a factor of four, who will the standard error change?
A. It will quadruple.
B. It will double.
C. It will be cut to 0.25 of 5.
D. It will be cut in half.
16) A pooled proportion estimate may be used to calculate the test statistic for a test of the equality of proportions when the
A. null hypothesis states that the two population proportions are equal.
B. populations are normally distributed.
C. samples are independently drawn from the populations.
D. sample sizes are small .
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Subject: Mathematics | Topic: Statistics | ID: 158557
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17) A test for equality of two variances has sample sizes n1 = 13 and n2 = 10. The degrees of freedom for the test are
A. 12 and 9.
B. 21.
C. 13 and 10.
D. 26.
18) If the paired differences are normal in a test of mean differences, the distribution used for testing is the
A. f distribution.
B. student t distribution.
C. chi-square.
D. normal distribution.
19) The purpose of designing a randomized block experiment is to reduce the between-treatments variation (SST) to more easily detect differences between the treatment means.
A. True
B. False
20) If we simultaneously examine the effects of two factors on the dependent variable, along with the effects of interactions between different levels of those factors, we are performing a three-factor analysis of variance.
A. True
B. False
21)Main effects are simpler to interpret when the test of the interaction term is not significant in a two-factor ANOVA.
A. True
B. False
22) Comparison of c means in a one-factor ANOVA is the same as using c repeated t-tests.
A. True
B. False
23) When the problem objective is to compare more than two populations, the experimental design that is the counterpart of the matched pairs experiment is called the randomized block design.
A. True
B. False
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Subject: Mathematics | Topic: Statistics | ID: 158558
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$ 5.0 |
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24) Two independent samples of 20 each from male and female students of a large university have been selected at random. To test for difference in the grade point average between male and female students, the most likely ANOVA to fit this test situation is the
A. chi-square test .
B. randomized block design.
C. two-factor ANOVA.
D. completely randomized design of the analysis of variance
25) The Wilcoxon signed rank sum test statistic is approximately normally distributed whenever the sample sizes are larger than
A. 40
B. 30.
C. 20.
D. 10 .
26)The appropriate measure of central location of ordinal data is the
A. mean
B. median .
C. mode.
D. all of these .
27) Statistical methods that require few assumptions, if any, about the population distribution are known as
A. All of these
B. free agent techniques.
C. parametric techniques.
D. nonparametric techniques.
28) The number of degrees of freedom in testing for normality is the
A. number of intervals used to test the hypothesis minus number of parameters estimated minus 2.
B. number of intervals used to test the hypothesis minus number of parameters estimated minus 1.
C. number of parameters estimated minus 1.
D. number of intervals used to test the hypothesis minus 1.
29) A recent study of 400 accidents that occurred on a Saturday night were analyzed. Information collected was the number of vehicles involved and if alcohol played a role in the accident. For cell (2, No), what is the difference between the expected frequency and the minimum expected frequency according to Cochran's Rule?
Role of Alcohol? Number of Vehicles Involved Totals
1 2 3
Yes 50 100 20 170
No 25 175 30 230
Totals 75 275 50 400
A. 153.125
B. 158.125
C. 170
D. 5
30) In the chi-squared goodness-of-fit test, if the expected frequencies ei and the observed frequencies fi were quite different, we would conclude that the
A. chi-squared distribution is invalid, and we would use the t-distribution. instead
B. alternative hypothesis is false, and we would reject it.
C. null hypothesis is true, and we would not reject it.
D. null hypothesis is false, and we would reject it.
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Subject: Mathematics | Topic: Statistics | ID: 158559
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31) How many runs are in the sequence TFTFFFFTTF?
A. 5
B. 4
C. 6
D. 2
32) For applications of the Kruskal-Wallis test, the alternative hypothesis to be tested is:
A. At least two population medians are the same .
B. All c population medians are different.
C. At least two population medians are different.
D. All c population medians are the same.
33) The distribution for Spearman’s rho is
A. x^2.
B. t
C. z
D. F
34) The value of the sum of squares for regression SSR can never be larger than the value of total sum of squares SST.
A. True
B. False
35) In regression analysis, if the coefficient of determination is 1.0, then the coefficient of correlation must be 1.0.
A. True
B. False
36)Two models were proposed for a simple regression of tree height on bark thickness, Model A: Height’ = 7.8*Bark + 37 and Model B: Height’ = 8*Bark + 35. Using the information and calculations below, which model is best?
Model A: Height’ = 7.8*Bark + 37
Tree ID Height (feet) Bark Thickness (millimeters) Predicted Height Error Squared Error
1 150 15
2 175 18 177.4 -2.4 5.76
3 225 21 200.8 24.2 585.64
4 200 23 216.4 -16.4 268.96
Model 8: Height’ = 8*Bark + 35
Tree ID Height (feet) Bark Thickness (millimeters) Predicted Height Error Squared Error
1 150 15 155 -5 25
2 175 18 179 -4 16
3 225 21 203 22 484
4 200 23
A. Model A.
B. Model B
C. The models are identical.
D. It is impossible to determine the best model.
37) The least squares regression line is obtained when the sum of the squared residuals is minimized.
A. True
B. False
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Subject: Mathematics | Topic: Statistics | ID: 158560
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$ 5.0 |
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38) The bivariate correlation coefficient always has the same sign as b1 in Y = b0 + b1X.
A. True
B. False
39) From the coefficient of multiple determination, we cannot detect the strength of the relationship between the dependent variable y and any individual independent variable.
A. True
B. False
40) If the coefficient of correlation is –0.81, then the percentage of the variation in y that is explained by the regression line is 81%.
A. True
B. False
41) An inverse relationship between an independent variable x and a dependent variable y means that, as x increases, y decreases, and vice versa.
A. True
B. False
42) In a simple linear regression model, testing whether the slope Beta1 of the population regression line could be zero is the same as testing whether or not the population coefficient of correlation p equals zero
A. True
B. False
43) Which of the following statements about multiple regression is TRUE?
A. If we have taken into account all relevant explanatory factors, the residuals from a multiple regression should be random.
B. The total sum of squares in a regression model will never exceed the regression sum of squares.
C. ratio of the regression sum of squares over the total sum of squares and subtracting that value from 1.
D. A multiple regression is called multiple because it has several data points.
44) If a group of independent variables are not significant individually but are significant as a group at a specified level of significance, this is most likely due to
A. the absence of binary variables.
B. multicollinearity.
C. the presence of binary variables.
D. autocorrelation .
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Subject: Mathematics | Topic: Statistics | ID: 158561
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45) Interpret the coefficient on gender.
A. Ceteris paribus: if a woman changes her gender, she will receive $9,290 less.
B. Ceteris paribus:a female is paid $9,290 less on average than a male.
C. Ceteris paribus: for each additional dollar of salary, a female’s salary moves 9.29 units closer to a male’s salary.
D. Ceteris paribus: a male is paid $9,290 less on average than a female.
46) If we want to measure the seasonal variations on stock market performance by quarter, we would need
A. 2 indicator variables.
B. 3 indicator variables.
C. 1 indicator variables.
D. 4 indicator variables.
47) The time series component that reflects variability over short, repetitive time periods that last less than one year is called
A. seasonal variation.
B. cyclical variation.
C. irregular variation.
D. long–term trend.
48) For which of the following values of the smoothing constant Alfa will the smoothed series catch up most quickly whenever the original time series changes direction?
A. 0.40
B. 0.90
C. 0.10
D. 0.50
49) Variations in output that are caused by specific temporary events such as machine malfunction are
A. special causes.
B. common causes.
C. out-of-control causes.
D. All of the these
50) When a change has occurred in the mean of the process distribution, the result is referred to as
A. a cycle.
B. a level shift.
C a trend.
D. instability
51) In statistical process control, a Type I error occurs if we decide that the process is
A. under control when it is under control.
B. under control when it is out of control.
C. out control when it is out of control.
D. out of control when it is under control.
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Subject: Mathematics | Topic: Statistics | ID: 158562
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$ 5.0 |
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