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In: Statistics and Probability

Q7: (About Interval Estimation: 2 marks) A coin is flipped 100 times, and 42 heads are...

Q7: (About Interval Estimation: 2 marks) A coin is flipped 100 times, and 42 heads are observed. Find a 99% confidence interval of π (the true population proportion of getting heads) and draw a conclusion based on the collected data. Hint: Choose the best one. (0.274, 0.536) a 99% confidence interval of π and we conclude it is a fair coin. (0.293, 0.547) a 99% confidence interval of π and we conclude it is a fair coin. (0.304, 0.496) a 99% confidence interval of π and we conclude it is a fair coin. (0.324, 0.486) a 99% confidence interval of π and we conclude it is a fair coin. (0.433, 0.509) a 99% confidence interval of π and we conclude it is a fair coin. (0.274, 0.536) a 99% confidence interval of π and we conclude it is not a fair coin. (0.293, 0.547) a 99% confidence interval of π and we conclude it is not a fair coin. (0.304, 0.496) a 99% confidence interval of π and we conclude it is not a fair coin. (0.324, 0.486) a 99% confidence interval of π and we conclude it is not a fair coin. (0.433, 0.509) a 99% confidence interval of π and we conclude it is not a fair coin.

Q8: (This continues Q7: 2 marks) Find the P-Value of the test. Ha: π =1/2. Vs. Ha: π ≠1/2. Less than 1%. Between 1% and 2% Between 2% and 3% Between 3% and 5% Between 5% and 8%

Between 8% and 10%
Between 10% and 12%
Between 12% and 15%
Between 15% and 20%
Bigger than 20%.

Expert Solution

given data are:-

sample size (n) = 100

sample proportion () = 42/100 = 0.42

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

the 99% confidence interval for the population proportion be:-

the correct option is:-

(0.293, 0.547) a 99% confidence interval of π and we conclude it is a fair coin

[ as 0.5 is contained in the interval we fail to reject the null hypothesis p =0.5 ]

8). the test statistic be:-

p value :-

[as this is a both tailed test]

[ using standard normal table]

the correct option is:-

the p value of the test is Between 10% and 12%

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orchestra answered 1 year ago

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