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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 Scenarios 4. 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 - multiplier value is larger than the z or t - multiplier value in 95% confidence interval implying that the 99% 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 is correct 16/25 times. Compute the 95% confidence interval on the proportion of times this person can predict coin flips correctly. What conclusion can you draw about this test of his ability to predict the future? The 95% confidence interval on the proportion of times is, 95% Confidence Interval = ቆ 𝑝 ̂ ± 𝑍 0 . 025 ∗ ට 𝑝 ො ∗ ( 1 ି 𝑝 ො ) ௡ ቇ = ቆ 16 25 ± 1 . 96 ∗ ට 16 25 ∗ ቀ 1 ି 16 25 ቁ 25 ቇ = (0.45184, 0.82816) The confidence interval contains the value 0.5. Now as this is a tossing problem so there are 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 provide evidence that the person has ability to predict the future . 15. You take a sample of 22 from a population of test scores, and the mean of your sample is 60. (a) You know the st and ard 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 = ቀ 60 ± 2 . 576 ∗ 10 √ 22 ቁ = (54.5079, 65.4921)

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