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expeople1 [14]
3 years ago
6

The latest poll from ESPN asked fans what their favorite sport was, considering pro, college and highschool levels. Out of 1000

fans, 32% of fans said their favorite sport was college basketball. Construct a 95% confidence interval.
Mathematics
1 answer:
shepuryov [24]3 years ago
7 0

Answer:

Confidence interval is 0.2911

Step-by-step explanation:

Given that 32% of fans sport is basketball as favorite sport. So total number of fans is,

32\%\times 1000

= \dfrac{32}{100}\times 1000

=320

So 320 fans favorite sport is basket ball.

Now find sample proportion ,

\widehat{p}=\dfrac{number\:of\:people\:in\:the\:sample}{total\:number\:of\:people}

Substituting the value,

\widehat{p}=\dfrac{320}{1000}

\widehat{p}=0.320

Formula for confidence interval is,  

CI=\widehat{p}\pm z\sqrt{\dfrac{\widehat{p}\left (1-\widehat{p}\right )}{n}}

To calculate the z value.

Confidence Level=1-\alpha

0.95=1-\alpha

0.05=\alpha

Now divide above value by 2,  

\dfrac{0.05}{2}=\dfrac{\alpha}{2}

0.025=\dfrac{\alpha}{2}

To find the value of z score calculate the area under the curve as follows

A=\dfrac{1+CL}{2}

A=\dfrac{1+0.95}{2}

A=\dfrac{1.95}{2}

A=0.975

On z table, find the value of 0.975. So the row corresponding to 0.975 is 1.9 and column corresponding to 0.975 is 0.06. Adding these two values the z score is 1.96.

or find the value from excel by using command as follows,  

=NORM.S.INV(0.025)= -1.959963985

Now substituting the value,  

CI=0.320\pm 1.96\sqrt{\dfrac{0.320\left (1-0.320\right )}{1000}}

CI=0.320\pm 0.02891

Lower end of the interval is,

CI=0.320- 0.02891

CI=0.2911

Upper end of the interval is,

CI=0.320+ 0.02891

CI=0.3489

Therefore 95% confidence interval is 0.2911

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