For questions 1 – 8, answer True or False. 1. The best point estimate for the po

Question

For questions 1 – 8, answer True or False.

1. The best point estimate for the population mean is the sample mean.

2. As the length of a confidence interval increases, the degree of confidence in its actually containing the population parameter being estimated (confidence level) also increases.

3. If the length of a confidence interval is very large, then the corresponding prediction is very meaningful.

4. A 90% confidence interval for a population mean implies that there is a 0.90 probability that the true population mean will be contained in the confidence interval.

5. A 90% confidence interval for a population parameter means that if a large number of confidence intervals were constructed from repeated samples, then on average, 90% of these intervals would contain the true parameter.

6. The point estimate of a population parameter is always at the center of the confidence interval for the parameter.

7. When repeated samples are selected from a population, the point estimate for a given parameter will always be the same value.

8. The larger the level of confidence, the shorter the confidence interval.

9. As the length of the confidence interval for the population mean increases, the degree of confidence in the interval’s actually containing the population mean _____.

10. If we change a 90% confidence interval estimate to a 95% confidence interval estimate, the width of the confidence interval will _____.

Explanation / Answer

1. The best point estimate for the population mean is the sample mean.

True , as the sample mean represents population mean based on central limit theorem

2. As the length of a confidence interval increases, the degree of confidence in its actually containing the population parameter being estimated (confidence level) also increases.

True , when the width of the CI increases then the confidence also increases as we become more confident that the true mean(or other statistic) would lie in the range

3. If the length of a confidence interval is very large, then the corresponding prediction is very meaningful.

False , as the length increases the range of the confidence interval also increases and the true point estimate gets a larger range of values which it can take

4. A 90% confidence interval for a population mean implies that there is a 0.90 probability that the true population mean will be contained in the confidence interval.

True , a 90% CI implies that we are 90% sure that the true value of the mean would lie in the range of the confidence interval

Please note that we can answer only 4 subparts of a question at a time , as per the answering guidelines

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