Question

The Harris Poll tracks the favorite sport of Americans who follow at least one sport. 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%. Consider 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 Baseball Men's college football Auto racing Men's professional basketball IceHockey OtherSports
111 39 46 14 6 20 108
Do college undergraduates students differ from the general public with regard to their favorite sports? Use x= .05.

Answer 1

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.