Respuesta :
Answer:
The calculated χ² = 20.779 falls in the critical region χ² ≥ 14.46 so we accept the null hypothesis that all the means are equal and college undergraduates students do not differ from the general public with regard to their favorite sports.
Step-by-step explanation:
1) We set up our null and alternative hypothesis as
H0: the college undergraduates students do not differ from the general public with regard to their favorite sport
H0: μ1= μ2=μ3=μ4= μ5=μ6=μ7=μ
against the claim
Ha: the college undergraduates students differ from the general public with regard to their favorite sport
2) The significance level alpha is set at 0.05
3) The test statistic under H0 is ( Pearson goodness of fit test )
χ²= ∑ (O - E)²/ E where O is the observed and E is the expected frequency
which has an approximate chi square distribution with 6 (n-1) d.f
4) Computations:
Under H0 , the observed frequencies are :
Observed Expected (O-E) (O-E)² (O-E)²/E
111 (0.33*344)=
113.52 -2.52 6.3054 0.0555
39 51.6 -12.6 158.76 3.0767
46 34.4 11.6 134.56 3.911
14 20.64 -6.64 44.0896 2.136
6 17.2 -11.2 125.44 7.293
20 17.2 2.8 7.84 0.4558
108 89.44 18.56 344. 4736 3.8514
344 20.779
5) The critical region is χ² ≥ χ² (0.025)6 = 14.45
6) Conclusion:
The calculated χ² = 20.779 falls in the critical region χ² ≥ 14.46 so we reject the null hypothesis that all the means are equal and college undergraduates students do not differ from the general public with regard to their favorite sports.
Given that all the results are lower or higher in percentage, but they do not exceed the 5.5% threshold, it can be said that college undergraduates students do not differ from the general public with regard to their favorite sports.
Since the Harris Poll tracks the favorite sport of Americans who follow at least one sport, and results of the poll show that professional football is the favorite sport of 33% of Americans who folllow at least one sport, followed by baseball at 15%, mens college football at 10%, auto racing at 6%, mens professional basketball at 5%, and ice hockey at 5%, with other sports at 26%, considering a survey in which 344 college undergraduates who follow at least one sport were asked to identify their favorite sport produced the following results:
- Professional Football = 111
- Baseball = 39
- Men's college football = 46
- Auto racing = 14
- Men's professional basketball = 6
- Ice Hockey = 20
- Other Sports = 108
To determine if college undergraduates students differ from the general public with regard to their favorite sports, the following calculation must be performed:
- Pro football = 111/344 = 0.3226 = 32.26% (-0.74).
- Baseball = 39/344 = 0.1133 = 11.33% (-3.67).
- Men's college football = 46/344 = 0.1337 = 13.37% (+3.37).
- Auto racing = 14/344 = 0.0406 = 4.06% (-2.94).
- Men's professional basketball = 6/344 = 0.0174 = 1.74% (-3.26).
- Ice Hockey = 20/344 = 0.0581 = 5.81% (+0.81).
- Other Sports = 108/344 = 0.3139 = 31.39% (+5.39).
Therefore, given that all the results are lower or higher in percentage, but they do not exceed the 5.5% threshold, it can be said that college undergraduates students do not differ from the general public with regard to their favorite sports.
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