Question

In the survey of 891 US adults who follow baseball in a recent year, 184 said that the Boston red sox would win the world series. Construct a 90% confidence interval for the population proportion of US adults who follow baseball who in a recent year said the Boston red sox would win the world series

Answer 1

Answer:

90% confidence interval for the population proportion of US adults who follow baseball

( 0.1842 , 0.22880)

Step-by-step explanation:

Explanation:-

Given data the survey of 891 US adults who follow baseball in a recent year, 184 said that the Boston red sox would win the world series.

The sample proportion $'p' = \frac{184}{891} = 0.20650$

                           q = 1-p = 1- 0.20650 =0.79350

Confidence intervals

90% confidence interval for the population proportion of US adults who follow baseball

$(p-Z_{\alpha } \sqrt{\frac{pq}{n} } , p + Z_{\alpha } \sqrt{\frac{pq}{n} } )$

The tabulated value Z₀.₉₀ = 1.645

$(0.20650-1.645\sqrt{\frac{0.20650X0.7935}{891} } , 0.20650 + 1.645\sqrt{\frac{0.20650X0.7935}{891} } )$

(0.20650 - 0.02230 , 0.20650+0.02230)

( 0.1842 , 0.22880)

Conclusion:-

90% confidence interval for the population proportion of US adults who follow baseball

( 0.1842 , 0.22880)