Question

A toy manufacturer has developed a new toy and now wants to know if the toy should be positioned in the marketplace as a toy for boys or for girls. In order to answer this research question, one of your colleagues observed a sample of boys and a sample of girls playing with the toy. For each child, your colleague recorded how long the child played with the toy before becoming bored. The collected data can be found below: Minutes played with the toy Boys 31 | 12 41 34 637 67 67 25 73 36 41 15 | Girls 26 38 20 32 16 45 9 9 16 26 81 20 5 The question now is, do boys or girls play longer with the toy on average? Your colleague feels a bit intimated by statistics but knows that you are not. Help your colleague answer the research question by conducting a pooled t test. Illustrate each of the 6 steps and be sure to state both your statistical and managerial conclusion. Use a 5% significance level. Hints: • We will conduct a “two sided” t-test, where the rejection region consists of a lower-tail region and an upper-tail region. The 5% significance level corresponds to the total area of the lower- and upper-tail combined. • With this statistical test you test for a difference between boys and girls. However, if you indeed find a significant difference, then you should be able to conclude which group is more likely to play with the toy longer. To draw this conclusion, examine the sign (+ or -) of your test statistic. • You can find the critical values for your test statistic's distribution in the statistical tables at the end of this problem set.

step 1 - set of hypotheses

step 2 - significance level

step 3 - test statistic and distribution (including degrees of freedom)

step 4 - rejection region (in words)

step 5 - statistical conclusion

step 6 - managerial conclusion

Answer 1

Grinds, A Let us played with the toy by Boy is the overage pay and elg is the overage played Meill Hypothesis Hot M = ela and Alternative Hypothesis Hill, i la = No. of timed mingle m = 1 » ) by played by the boys. = 13 the barls='rs. Text Statistics. (-7) - (-e): No No when, eg, - (- ) N(011) mn This statistic cel can we test statistich because s is canknown and then we put Estimate of s.. where, he is the men of minutes played by boys ? i is the mean of minutes played by Gubles e is the warrince Now. m-13 Sage Emel (-1)S? a or ma independent
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→ Am. -1 382 + (1.–1 ) 53 ~ My on tos-2 EC SP=871 - - - - ) 3 + (n-1) SS comtm-2) Cunbiated Eltimate off Esta potted sample variana 31 32 -5.30462 Then the Test Statistico copa v mm (7-7), v tomto -2 mth Sp How Reject Ho if Itir Emm-2, & Boyd, brises. Ix-X. 1 y 7 (xxl | 4.72 26 7-8.385 10:38 469 170-308 0.1479 19. 38 -27.385 11.61538 1749.9/74. 1134.9171 2011.695 1-6.38462 2.609453 140.76337 |-5.30462 5.6153828.99913 31.53249 23.6153 710.3846 557. 6062 107.8903 |-39.384 110.61530 1040.764346. 5394 27.6158 17.3846669.6092 1309. 5394 g ev 29.6153-17238761762.6092 309.225 16. 1-1438461-40-38461206.9173 1107.-8403 2 6 33.6153 Tomorce 11.29.994 10.197933 43,38962:54. 6153411-45565 2989.84 26 11.61538 76-38462/2.60943 140.76337 5 192138961-21-3846 594.6097 459.309 343 3 5929.077 | 4855.077 45 4-1 15 512 189 toul 1x3 8-9512-7= 39.385, 7:= 343. = 36+385
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5 = E(; -pję sånt. 14-)? x 98851077 S; -o- * 5329.077 ) Se | sã = 904.5897 so = 499.0897 Polled Sample variance Sie = (om,-1,54+ (m-195 (m+n-29 =12*494.08977 404,5897 XIX (13+13-2) sa - 449.3397) [Sp= 31-1976) test statistic value. 171 = avro ( ) min 171 = D 0.5 X /39.38469-2630462) 21.1976 Grinen, significance del & -sr. 2o .SX 13 0. 30 664 Litmana a 9 Jetman-2, RS? 1 tablelated value Honei 1414 9.064. ) +94, sy, - tq q, 0.0% t22, 0.095 – 2.064 the null hypothers. lations thats mem, overge time of Boys and Girl are some 21.1976 (T) =0.30 60D w so, we fail to dreject to
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