Econ 2500 Section E 3.0 - Fall 2015 Assignment 1 (Due Date: October 8, 2015) Question 1: At the PISA Web site (www.pisa.oecd.org), there are summary statistics for math scores of 15-year-old males and females for various countries separately. The mean math scores for males, the mean math scores for females, and also the dierence of the two means are listed in the Excel le. a. Use any software and obtain the histogram for the mean math scores for males. b. How would you describe the overall shape of this data set? Do you suspect any outlying group in this data set? c. Report the 5-number summaries for the dierence of the two means. (Note: Don't use software. Use the method discussed in class). d. Obtain the back-to-back stemplot and compare the distribution of the mean math scores for males and for females. e. Use any software and report the sample mean and sample standard deviation for the mean math scores for females. f. Based on the given data, what proportion of the mean math scores for females falls within 2 standard deviation of the mean? Question 2: It is well-known that the relationship between degree Fahrenheit (F ) and degree Celsius (C) is 9 F = C + 32 5 We randomly selected 100 days in October from 2010-2014 and recorded the temperature (in degree Fahrenheit) of New York City. We have the following summary statistics from R: Min. 66.00 1st Qu. 73.00 Median 76.50 Mean 76.55 3rd Qu. 79.00 Max. 92.00 std dev 5.015884 Report the summary statistics in degree Celsisus. Question 3: The amount of sodium is recorded for each of the 200 randomly selected 9-ounce serving of chicken noodle soup which yields a mean of 1100 mg and a standard deviation of 150 mg. Moreover, the data distribution looks approximately bell-shaped. a. Approximatelhy, what proportion of soups have amount of sodium is less than 950 mg? b. Approximatelhy, what proportion of soups have amount of sodium is between 800 mg and 1550 mg? 1 c. An expert said that when the amount of sodium is 6 standard deviation higher than the mean, it is then considered to be dangerous. In this case, what amount (in mg) is considered to be dangerous? Question 4: Consider the follow split stem-and-leaf plot of 52 data points: Leaf unit = 0.1 1 12 1 668 2 04 2 888 3 1334 3 555778899 4 0000111233444 4 56788 5 222 5 779 6 03 6 6 7 2 7 8 8 9 R gives the following summary statistic: Min. 1.100 1st Qu. 3.375 Median 4.000 Mean 4.060 3rd Qu. 4.725 Max. 8.900 Also the sample variance is reported to be 2.1570. a. What percentage of data falls below 3.0? b. Based on the R output, identify all outliers and extreme outliers? c. Is Empirical Rule applicable here? Why or why not? d. What do the Empirical Rule and Chebyshev Rule said about the percentage of data fall within 2 standard deviation of the mean? How about the actual percentage of data fall within that range? e. Find the z-score for the largest and smallest data points. 2 Question 5: Many people grab a granola bar for breakfast or for a snack to make it through the afternoon slump at work. For the Kashi GoLean Crisp Chocolate Caramel 45 grams bar, the company claimed that the mean amount of protein in each bar is 9 grams with a standard deviation of 1.5 gram. Suppose the distribution of protein in a bar is normally distributed. a. What is the probability that the amount of protein is less than 7.75 grams? b. What is the probability that the amount of protein is between 7.8 and 8.2 grams? c. Suppose the amount of protein is at least 8.1 grams. What is the probability that it is more than 8.3 grams? d. What is the amount of protein that is exceeded by 2.5% of all the bars? Question 6: The types of books borrowed by 36 randomly selected students from York University are: Psychology Science Education Law Technology Science Psychology Literature Literature Psychology Literature Technology Technology Literature Science Literature Psychology Law Education Technology Science Education Law Technology Education Psychology Law Law Psychology Literature Education Technology Science Education Law Education a. Obtain a bar chart using relative frequency on the vertical axis. b. Obtain a pie chart for this data set. c. Do you think the York University should try to acquire more books in one particular subject area? Why or why not? Question 7: Three of the following students will form the Executive Committee for the York University Students Council: Annie Charles Darwin Ellen Ginny Justin Kerri Mandy Steve Zach It was decided that the following random digits will be used to help to choose the committee. 09297 00412 71238 60500 14873 07095 08709 Clearly explain who will be on the committee. 3 bin limit Males 527 517 524 534 514 518 554 499 513 462 496 503 507 470 533 552 498 410 537 527 493 500 474 499 484 505 536 427 504 479 554 410 30 503.2 Females Difference 513 14 494 23 517 7 520 14 504 10 508 10 543 11 492 7 494 19 457 5 486 10 508 -5 496 11 453 17 513 20 543 9 482 16 401 9 524 13 517 10 487 6 491 9 459 15 485 14 476 8 500 5 523 13 421 6 487 17 470 9 0 0 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 Histogram 7 Frequency Question 1 data: Country Australia Austria Belgium Canada Czech Republic Denmark Finland France Germany Greece Hungary Iceland Ireland Italy Japan Korea Luxembourg Mexico Netherlands New Zealand Norway Poland Portugal Slovak Republic Spain Sweden Switzerland Turkey UK USA highest value lowest score Number N mean 6 5 4 3 2 1 0 0 More Frequency 1 0 1 0 0 0 2 2 1 6 4 4 2 4 0 2 0