Solution to Test #1.

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1 Solution to Tet #. Problem #. Lited below are recorded peed (in mile per hour, mph) of randomly elected car on a ection of Freeway 5 in Lo Angele. Data are orted A. Finih the following table: Cla Relative Frequency Cumulative Frequency Data Frequency (give anwer a reduced fraction) = = = SUM N/A (Do not Fill thi pace)

2 B. What number appear mot frequently? What i the frequency? 73 appear mot frequently, it frequency i 6 C. What i the mode? 73 D. What i the range? max min E. What i the midrange? max min midrange F. What i the median? There are two number in the middle, the 0 th, 68 and the t, 70, o the median i You might need thee number: The um of all the number: x 735 The um of quare: x x x 375 G. What i the mean peed x for thi random ample? (Round to the nearet thouandth.) 735 x x n H. What i the variance of the random ample? (Round to the nearet thouandth.) n x n n x x n x I. What i the tandard deviation of the random ample? (Round to the nearet thouandth.) n x n n x J. What i the percentile of data value 70? (Round to the nearet whole number.) There are 0 number that are maller than 70, o 0 The percentile of data value K. Find the firt Quartile, that i the 5 th percentile number in the data et, P5 Q.

3 L The tenth number i 65 and the eleventh number i 65, o Q P 65 5 L. Find the third Quartile, that i the 75 th percentile number in the data et, Q3 P75. L The 30 th number i 73 and the 3 t number i 73, o Q P 73 M. Find P 0 0 L The 4 th number i 59 and the 6 th number i 60, o P N. Find P 90 L The 36 th number i 75 and the 37 th number i 75, o P O. Find the inter-quartile range IQR? (definition in text book page 0): IQR Q3 Q P. Find the emi-inter-quartile range, (definition in text book page 0): Q Q Q. Find the mid-quartile: (definition in text book page 0): Q Q R percentile range: (definition in text book page 0): P 90 P S. Contruct a Box Plot for thi et of data. (Refer to example in the text.)

4 T. The word uual i for any data that fall within two tandard deviation of the mean, what i the uual range of peed? Give the range a an interval. x x , The uual range of peed i U. According to Chebyhev Theorem, at leat what percentage i expected to be in the uual range you jut calculated? At leat 75% i expected to be in the uual range of , V. Extra credit quetion: What i the actual percentage of number from thi data et that fall within the uual range that you jut calculated? There are actually 39 number fall within tandard deviation of the mean, here i the percentage: % Problem. The following table repreent a frequency ditribution of the duration time of (in econd) of eruption of the Old Faithful Geyer. From the information given in the table, fill out the 5 blank pace with the right number, repectively. Lower Cla Duration(Second) Upper Cla Cla Boundarie Lower Limit Upper Limit Boundarie Frequencie Midpoint >> Problem 3. If the Empirical Rule applie for all the IQ core, and we know the population mean and tandard deviation for all the IQ are 00, 5, repectively. Anwer the following quetion: a. What percentage of IQ core i between 85 and 5?

5 That i within one tandard deviation of the mean. According to Empirical Rule, 68% of the IQ are between 85 and 5. b. What i the uual range of IQ core? Give your anwer a an interval. The uual range i defined a within two tandard deviation of the mean, which i x x The uual range of IQ core i 70,30 c. Thoma Edion IQ core i 45, but that matter only % of the time becaue geniu i % inpiration and 99% perpiration. I hi IQ conidered uual or unuual if ABOVE three tandard deviation of the mean IQ core i conidered Geniu? Explain. x IQ core ABOVE 45 i then conidered Geniu. Since Thoma Edion IQ core i 45 which i NOT ABOVE the 45 threhold. Thu, he i not a geniu according to thi criterion. However, geniu i % inpiration and 99% perpiration, according to him. Problem 4. Lited below are the budget (in million of dollar) and the gro receipt (in million of dollar) for randomly elected movie. Budget x Gro Receipt y x SUM x 68 y 00 x 750 y xy y xy a. Compute the correlation coefficient r. Round the anwer to the nearet thouandth (three decimal place).

r n n xy x y x x n y y 7 49733 6800 7 750 68 7 37908600 0.936 b. Find the critical value from the table in Page 760 for the ignificance level of α = 0.05. Critical Value are ±0.754 for n = 7, α = 0.

6 r n n xy x y x x n y y b. Find the critical value from the table in Page 760 for the ignificance level of α = Critical Value are ±0.754 for n = 7, α = 0.05 c. Could we conidered the two variable, x and y linearly correlated? Why? We could conider that the two variable are linearly correlated ince r i bigger than and i maller than. d. Extra credit, find the linear regreion line uing the formula in ection 0.3 for the lope and y-intercept. b n xy x y n x x b 0 y x x xy n x ŷ = x OR: Ue thee formula: y b0 y rx x b r

7 00 y 68 y x x n 7 n 7 y x b y r x b 0 y rx e. Extra credit, make a prediction according to the linear regreion line you have found in c. for a budget of 00 million, what might be the value etimated for the Gro Receipt? Show all your calculation. Problem 5. (0 point) With a height of 75 inche, Lyndon Johnon wa the tallet preident of the pat century. With a height of 67 inche, William McKinley wa the hortet preident of the pat century. With a height of 85 inche, Shaquille O Neal i the tallet player on the Miami Heat Baketball team. The mean height of the Preident in the pat century i 7.5 inche and a tandard deviation. inche. The mean height of the Baketball player for the Miami Heat i 80 inche and a tandard deviation 3.3 inche. a. What i the z-core of Lyndon Johnon? x Lyndon Johnon:. 67. b. What i the z-core of William McKinley if the mean height of the Preident in the pat century i 7.5 inche and a tandard deviation. inche? x William McKinley:. 4. c. What i the z-core of Shaquille O Neal? x Shaquille O Neal d. Who i relatively taller: Lyndon Johnon among the preident of the pat century, or Shaquille O Neal among the player on hi Miami Heat Team? Explain.

8 Lyndon Johnon height i.67 tandard deviation above the mean, and Shaquille O Neal height i.5 deviation above the mean. Lyndon Johnon height among preident of the pat century i relatively greater than Shaquille O Neal height among the Miami Heat baketball player. Shaquille O Neal i much taller than Lyndon Johnon, but Johnon i relatively taller than when compared to hi colleague.

Social Studies 201 Notes for November 14, 2003

Social Studies 201 Notes for November 14, 2003 1 Social Studie 201 Note for November 14, 2003 Etimation of a mean, mall ample ize Section 8.4, p. 501. When a reearcher ha only a mall ample ize available, the central limit theorem doe not apply to the