江西财经大学国际学院统计学试卷A

江西财经大学国际学院统计学试卷A

1. Single selection (1 point per question, 10 points total) 1. A partial relative frequency distribution is given. Class Relative Frequency G 0.22 F 0.18 H 0.40 K

The total sample size is 200. The frequency of class K is ( A ). A 40 B 50 C 60 D 80 2. If the data are moderately skewed left, ( B ) A MoMex B xMeMo C xMeMo D MoxMe

3. The ( C ) is the value in the middle when the data are arranged in ascending order.

A mean B mode C median D quartiles 4. Assuming the student test score is normal distributed, X~N78,64，Then about 68.26%（Z＝1）test score fall in the interval of ( B )

A (70，80) B (70，86) C、(62，94) D（80，86） 5. How large a sample should be selected to provide a 95% confidence interval with a margin of error of 10? Assume that the population standard deviation is 40.( C )

A 60 B 61 C 62 D 59

6. Which regression equation below is wrong? r is the correlation coefficient( C )

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ˆ23x r=0.9 A yˆ45x r=0.55 B yˆ105x r=－0.85 C yˆ1000.90x r=－0.83 D y7. The total retail sales increased by 20% than the previous year in an area. Eliminate the impact of price, the real total retail sales increased 11%, then the price index in this area should be ( D )

A 9% B 8.1% C 109% D 108.1%

8. According to the properties of the mean, which is true of the following expressions?( A )

A．(xx)f0 B．xxf0 C．(xx)2f0 D.

(xx)fmin

price Index of the following index（ B ）.

9. If p stands for commodity price，q stands for sales，which is the Pacsche

pqA.pq B.pq C.p1q0D.01

p0q0pqpqp0q0

1111000110. If we know the r2 of a linear regression is 0.64, then the residual sum of squares occupies a proportion of ( A ) in the total sum of squares. A 0.36 B 0.8 C 0.6 D 0.2

2. True or False (1 point per question, mark“T”behind the true statements, “F” behind the false statements.10 points total)

1. The scale is interval if the data demonstrate the properties of nominal data and the order or rank of the data is meaningful. ( F ) 2. The quartiles can be used to divide a data set into three parts, with each part containing approximately 25% of the data ( F ) 3. for overlapping class limits, the frequency distribution follow the principle of “the upper class limits are not in the same class”. ( T ) 4. To estimate the value of a population parameter, we compute a corresponding characteristic of the sample, referred to as a sample statistic.

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( T )

5.α is the probability of making a Type II error by rejecting H0 when the null hypothesis is true. （ T ） 6. The confidence level is the probability that the unknown population parameter falls within Interval. ( T ) 7. The symbol of the correlation coefficient represents the relationship between x and y is positive or negative, the absolute value of the correlation

coefficient represents the strength of the correlation between x and y.( T ) 8. Least squares method is by making the maximum residual sum of squares

to estimate the regression coefficients. ( F ) 9. Laspeyres index is the weighted aggregate index which the weights are

based on the indicator in reporting period. ( F ) 10. If the data seems to have an upward secular trend，the seasonal index of

the end of the year is larger than the one of the beginning of the year. ( T )

3. Question and answers (16 Points total, 28=16 Points) 1. Describe briefly the components of a time series.

2. Describe briefly the selection of the weights in making general index.

4. Calculation (45 points)

1. In an industrial enterprise, the output per year and the number of the workers in the beginning of the year are listed below:

Output(million yuan) The number of the workers in the 2010 2018 2070 2120 2200 2007 2008 2009 2010 2011 565 597 614 636 beginning of the year 3

Question: The average annual workers number and the average annual labor productivity are calculated in the following. Please make your judgment whether it is right. If you think it is wrong, please correct it. (15 points)

The average annual workers number:

y0y20102120y1y2yn1n201820702221538 y2n4The average annual labor productivity

a＝(565597614636)/4=0.39（million yuan per person）

1538

3. (15 points) You’re an accounting manager. A year-end audit showed 4% of transactions had errors. You implement new procedures. A random sample of 500 transactions had 25 errors. Has the proportion of incorrect transactions changed at the .05 level? (z0.0251.96,z0.051.65,

z0.0052.58)) Solution H0: p=4% H1: P≠4% Z=

3. (15 points) The price and volume of 3 products are listed below:

Product A B C Volume 2008 20 40 60 2009 30 40 65 Price 2008 10 20 25 2009 15 25 30 Question: Using the index system, analyze the impacts that the changes of

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volume and price have caused the revenue, with both the relative numbers and the absolute numbers. 5. Case study (19 Points)

The enrollment data (in thousands) for a state college over the past six years are shown.

Year 2005 2006 20.2 2007 19.5 2008 19.0 2009 19.1 2010 18.8 Enrollment 20.5 (1) Develop the equation for the linear trend component of this time series. (2) Comment on what is happening to enrollment at this institution. (3) What is the forecast for 2011?

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