maggie9459

04.05.2021 •

Mathematics

Which expression cannot be evaluated? a) P(100, 98)
b) 100!/98!
c) 98!/100!
d) P(98,100)

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Ответ:

cadeduncan71

13.03.2020

Mathematics

The confidence interval is 0.41 < p < 0.45

Generally the 95% confidence interval mean that there is 95% confidence that the true proportion of US adults who regularly watch television shows through streaming fall within the confidence interval

As the sample size increase from 2300 to 5000 the confidence interval becomes narrower

Step-by-step explanation:

From the question we are told that

The sample proportion is $\^ p = 0.43$

The sample size is n = 2300

From the question we are told the confidence level is 95% , hence the level of significance is

$\alpha = (100 - 95 ) \%$

=> $\alpha = 0.05$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} }$

=> $E = 1.96 * \sqrt{\frac{ 0.43 (1- 0.43 )}{2300} }$

=> E = 0.020

Generally 95% confidence interval is mathematically represented as

$\^ p -E < p < \^ p +E$

=> 0.43 -0.020 < p < 0.43 + 0.020

=> 0.41 < p < 0.45

Now when the sample size is increase to 5000 the margin of error becomes

=> $E_1 = 1.96 * \sqrt{\frac{ 0.43 (1- 0.43 )}{5000} }$

=> E_1 = 0.0137

So as we can see E_1 < E hence the confidence interval becomes narrower

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Which expression cannot be evaluated? a) P(100, 98) b) 100!/98! c) 98!/100! d) P(98,100)