Students who are home-schooled often attend their local schools to participate i

Question

Students who are home-schooled often attend their local schools to participate in various types of activities such as sports or musical ensembles. According to the government, 82% of homeschoolers receive their education entirely at home, while 12% attend school up to 9 hours per week and 6% spend from 9 to 25 hours per week at school. A survey of 85 students who are home-schooled revealed the following information about where they receive their education. At alpha = 0.05, is there sufficient evidence to conclude that the proportions differ from those stated by the government? USA TODAY reported that 21% of loans granted by credit unions were for home mortgages, 39% were for automobile purchases, 20% were for credit card and other unsecured loans 12% were

Explanation / Answer

for above applying chi square goodness of fit

here degree of freedom =(n-1)=2

and test stat chi square =31.7504

for 2 degree of freedom and 0.05 level of significance; critical value =5.991

as chi stat is higher then critical value; we reject null hypothesis and conclude that p[roportions differs from those stated by the government

observed Expected Chi square Probability O E=total*p =(O-E)^2/E ent at home 0.820 50.000 69.70 5.57 up to 9hours 0.120 25.000 10.20 21.47 9-25 Hours 0.060 10.000 5.10 4.71 1 85 85 31.7504

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