28.1 The data in Table 28.3 represent salaries (in pounds Sterling) in 72 randomly selected advertisements in the The Guardian (April 6, 1992). When a range was given in the advertisement, the mi...
28.1 The data in Table 28.3 represent salaries (in pounds Sterling) in 72 randomly selected advertisements in the The Guardian (April 6, 1992). When a range was given in the advertisement, the midpoint of the range is repro- duced in the table. The data are salaries corresponding to two kinds of occu- pations (n m-72): (1) creative, media, and marketing and (2) education. The sample mean and sample variance of the two datasets are, respectively: (1) i72=17410 and s2= 41 258 741. (2) 19818 and s 50744521 Table 28.3. Salaries in two kinds of occupations Oceupation (1) Occupation (2) 17703 13796 12000 25899 17378 19236 42000 22958 22900 21676 1554 187S0 18780 10750 13440 15053 17375 12459 15723 13502 17574 19461 20111 22700 3179 21000 22149 22185 16799 33730 37500 18245 17547 17378 12587 20339 22935 19358 9300 15053 24102 13115 13000 22000 23000 108 I273 13603 13500 12000 15723 18360 35000 2039 13000 16820 12300 22333 20900 16629 1000 17T09 1075S0 23008 13000 27500 12300 23063 11000 24260 18006 I7378 13000 18693 19000 25899 33103 15033 10300 14472 13300 21 17378 20091 12285 12000 32000 17970 14855 9866 13000 20000 T83 210 210T4 21074 1%0014181 180xx) 20739 15053 150.53 3944 35000 11406 15053 15083 31530 23960 18000 23000 30800 102 16799 11389 30000 15379 37000 11389 13053 2587 12318 21438 48000 11389 14359 17000 17048 21262 1000 26544 15344 000 13349 20000 20147 14274 31000 Souree: D.J. d, F. Daly,AD. LE,KJ. MeConway, and E Ostroms Small dafe aets Chapman and Hall, Loadon, 1994 dataet 385 Data col lected by D J. Hand Suppose that the datasets are modeled as realizations of normal distribations with expectations n and 4e2, which represeณt the salaries for occupations (1) and (2) a. Test the null hypothesis that the salary for both occupations is the same at level a 0.05 nder the assumption of equal variances. Formulate the proper null and alternative bypotheses, compute the value of the test statistie, and report your conclusion b. Do the same without the assumption of equal variances c. As a comparison, one carries out an empirical bootstrap simulation for the nonpooled studentized mean difference. The bootstrap approximations for the critical values are 2.004 and -2.133. Report your conchısion about the salaries on the basis of the bootstrap results.
28.1 The data in Table 28.3 represent salaries (in pounds Sterling) in 72 randomly selected advertisements in the The Guardian (April 6, 1992). When a range was given in the advertisement, the midpoint of the range is repro- duced in the table. The data are salaries corresponding to two kinds of occu- pations (n m-72): (1) creative, media, and marketing and (2) education. The sample mean and sample variance of the two datasets are, respectively: (1) i72=17410 and s2= 41 258 741. (2) 19818 and s 50744521 Table 28.3. Salaries in two kinds of occupations Oceupation (1) Occupation (2) 17703 13796 12000 25899 17378 19236 42000 22958 22900 21676 1554 187S0 18780 10750 13440 15053 17375 12459 15723 13502 17574 19461 20111 22700 3179 21000 22149 22185 16799 33730 37500 18245 17547 17378 12587 20339 22935 19358 9300 15053 24102 13115 13000 22000 23000 108 I273 13603 13500 12000 15723 18360 35000 2039 13000 16820 12300 22333 20900 16629 1000 17T09 1075S0 23008 13000 27500 12300 23063 11000 24260 18006 I7378 13000 18693 19000 25899 33103 15033 10300 14472 13300 21 17378 20091 12285 12000 32000 17970 14855 9866 13000 20000 T83 210 210T4 21074 1%0014181 180xx) 20739 15053 150.53 3944 35000 11406 15053 15083 31530 23960 18000 23000 30800 102 16799 11389 30000 15379 37000 11389 13053 2587 12318 21438 48000 11389 14359 17000 17048 21262 1000 26544 15344 000 13349 20000 20147 14274 31000 Souree: D.J. d, F. Daly,AD. LE,KJ. MeConway, and E Ostroms Small dafe aets Chapman and Hall, Loadon, 1994 dataet 385 Data col lected by D J. Hand Suppose that the datasets are modeled as realizations of normal distribations with expectations n and 4e2, which represeณt the salaries for occupations (1) and (2) a. Test the null hypothesis that the salary for both occupations is the same at level a 0.05 nder the assumption of equal variances. Formulate the proper null and alternative bypotheses, compute the value of the test statistie, and report your conclusion b. Do the same without the assumption of equal variances c. As a comparison, one carries out an empirical bootstrap simulation for the nonpooled studentized mean difference. The bootstrap approximations for the critical values are 2.004 and -2.133. Report your conchısion about the salaries on the basis of the bootstrap results.
