Question

When games were randomly sampled throughout the season, it was found that the home team won 127 of 198 professional basketball games, and the home team won 57 of 99 professional football games.
      a) Find a 95% confidence interval for the difference in the population proportions of home wins. Include the sample proportions, z α 2and standard error.
b) Based on your results in part a) do you think there is a significant difference? Justify your answer; explain.

Answer 1

i am denoting the professional basketball group by 1 and professional football group by 2.

given data and necessary calculations are:-

z critical value for 95% confidence level, both tailed test be:-

the standard error be:-

  

the 95% confidence interval for the difference in the population proportions of home wins is :-

b). I think there is no significant difference. Because 0 is included in the 95% confidence interval.