Question

A theme park owner wants to know if the children's rides are favoring 10 year old girls over 10 year old boys based on height. In other words, is one group taller than the other and thus can go on more rides? (Note: amusement parks determine whether someone can go on a ride based on height.) Part a: The owner gathered height data on 10 year old girls and 10 year old boys, see excel document for data. Determine at the 5% significance level if there is evidence that the two genders are not the same height. Show your work and give your answer in complete sentences in context of the problem. What does this mean about 10 year old kids who may want to go on an amusement park ride? Part b: After doing some research, the owner found the following information about the expected height and standard deviation for 10 year olds. Does that change the result of part a? Show your work and give your answer in complete sentences in context of the problem. 10 year old girls 10 year old boys Average height 54.5 inches 54.5 inches St. deviation 2.74 inches 2.71 inches

Answer 1

Answer Null hybothesis : - There is no significant difference betroren the two mean Alten othesis: - There is a signifirant difference a between the two mean 10 yecer old girls, 0:22 mecin 54.4045 osid (standard deviation ) : 2160052 10 year old baly :- n; 18 mean> 5413611 Sid (Standard deviction ) :2.827830 Case 1 equal vagulance sumed to ř - ý sottt ni na n tntna-2 si pan so = van ( nit tvorcy (n2-1) nitna-2 54.404 S. 54.311 17 - od to 3d = (216209 ) "azd ? (2.694 70) *! 2.1992 2.71522 + (21829630) 1(2162092) X2 sd T2.62052) x2 38

:,043430 oso to 043230 2, 71522031762 01 %6295 tabulated t = t38,005 ; +38,00QS = 2.0244 As Calculated t Cooso) < tabulated t(210244 ) thus we fail to dreject the null hypothesis thus there is no significant difference between a means is no

qual vorulunces are not assumed t: B- ate f( degree of freedom) = Sy? & fredum s r 5x² phere on these f: 35.210 35 + 36 54.4045 - 54.3611 2.62052) + (21827430) ਦੀ ਕ੨ 18 0.043430 0.46971 : 050234 Calculated to 0 50234 tabulated t : +35,0025 - 20301 AS calculated + Coroso ) <tabulat end +(210301) thus we fail to reject the null hypothesis this thop is no - Significant difference between two means. 4 This means that both girls and boys has ean as equal access to - all the sides and any of the lo year old kid - to any en amusement park side 3 and any of the lo year old kid may goon

Part b new data- girls boyg Audruge height 54:5 54.5 St. d furiation 2.74 2171 As there is no difference between the average Sample height, we can say that there is no significant clippere between the heights. Thus it does not change the result of part a As . t= 7- ų ntoitno-2 soft, as Ž - ÿ => 54.5 - 5415 Thus too t This calculated oculated t tabulated t, thus this we fail to reject the null hypothesis thus there is no Wificant difference between the heights or lo geasold girl and boy