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Homework Week 5 : Understanding Confidence Intervals and Statistical Analysis in Real-World Scenarios

Homework on confidence intervals and statistical analysis.

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Homework Week 5: Understanding Confidence Intervals and Statistical Analysis in Real-World Scenarios4.Why is a 99% confidence interval wider than a 95% confidence interval?The formula for constructing the Confidence interval is,Confidence Interval = (Mean ± Z-multiplier*Standard error)or (Mean ± Z-multiplier*Standard error)Now while calculating the 99% confidence interval the Z or t-multipliervalue is largerthan the z or t-multiplier value in 95% confidence interval implying that the99%confidence interval wider than a 95% confidence interval.12.A person claims to be able to predict the outcome of flipping a coin. This person iscorrect 16/25 times. Compute the 95% confidence interval on the proportion of times thisperson can predict coin flips correctly. What conclusion can you draw about this test ofhis ability to predict the future?The 95% confidence interval on the proportion of times is,95% Confidence Interval =á‰†đ‘Ì‚Â±đ‘0.025âˆ—à¶§đ‘à·œâˆ—(1àŹżđ‘à·œ)àŻĄá‰‡=ቆ1625±1.96∗ට1625∗ቀ1àŹż1625ቁ25ቇ= (0.45184, 0.82816)The confidence interval contains the value 0.5. Now as this is a tossing problem so thereare two outcomes and on any random guess we have 0.5 probability to guess correctly.And as the probability 0.5 is within the confidence interval so the data does not provideevidence that the person hasability to predict the future.15.You take a sample of 22 from a population of test scores, and the mean of your sample is60.(a)You know the standard deviation of the population is 10. What is the 99%confidence interval on the population mean.The 99% confidence interval on the population mean is,99% CI =ቀ60±2.576∗10√22ቁ= (54.5079, 65.4921)

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