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.

2. The level of confidence that a confidence interval contains the population parameter being estimated increases as its length does (confidence level).

→ True, when the CI widens, our confidence grows as well since we are more certain that the true mean (or another statistic) will fall inside the range.

3. If a confidence interval is very long, it means that the corresponding prediction is highly significant.

→ False, as the length increases, the confidence interval's range similarly expands, giving the correct point estimate a wider range of possible values.

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

→ True, a 90% CI means that we are 90% confident that the range of the confidence interval contains the true value of the mean.

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.

→ True, 90% of the values attains positive values.

6.A population parameter's point estimate is always in the middle of the parameter's confidence interval.

→ It is true that the sample statistic, such as a sample mean or sample proportion, is at the center of a confidence interval. The point estimate is what is used here. The margin of error determines the width of the confidence interval.

7. A population's point estimate for a particular parameter will always be the same when repeated samples are taken from it.

→ False.

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

→ False, an increase in the margin of error follows an increase in the level of confidence. A broader confidence interval is produced by a higher margin of error.

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