Question

In a simple random of 400 of Deadpool fights, Deadpool breaks the Fourth Wall in 230 of them.

(a)A 99.9% confidence interval for the true proportion of all fights in which Deadpool breaks the fourth wall is ( , ) (Answers to four places after the decimal.)

(b) Unless our sample is among the most unusual 1% of samples, the true proportion of all fights in which Deadpool breaks the fourth wall is between ( ) and ( ) . (Answers to four places after the decimal.)

(c)Vanessa claims that Deadpool breaks the Fourth Wall in half of his fights. Do we have evidence that she's underestimating the truth at each of the following levels?
The associated p-value for this hypothesis test is ( ) (Answers to four places after the decimal.)

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Answer 1

given data and some calculations:-

sample size (n) = 400

sample proportion () = 230/400 = 0.575

a).z critical value for 99.9 % confidence level, both tailed test be:-

the 99.9 % confidence interval for the true proportion of all fights in which Deadpool breaks the fourth wall is :-

b). unless the value is in the most unusual 1% of samples, that is we have to find (100-1) = 99% confidence interval

z critical value for 99 % confidence level, both tailed test be:-

the 99 % confidence interval for the true proportion of all fights in which Deadpool breaks the fourth wall is :-

Unless our sample is among the most unusual 1% of samples, the true proportion of all fights in which Deadpool breaks the fourth wall is between 0.5113 and 0.6387

c).hypothesis:-

test statistic be:-

The associated p-value for this hypothesis test is:-

[using standard normal table]

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