William H. Knapp III

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This homework was due on Friday, November 9 at 06:00 a.m. Turkish time. Late submissions receive half credit.

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1. A biased estimate of a population parameter.
Cannot be adjusted to provide an unbiased estimate.
Consistently under or overestimates the value of a population estimate.
Has a smaller variance than an unbiased estimate.
All of the above.

2. The sample mean is a biased estimate of the population mean.
True
False
It depends

3. The sample mean will always give you the correct value of the population mean.
True
False
It depends

4. The sample variance ________ estimates the population variance.
unbiasedly
over
under

5. To create an unbiased estimate of the population variance, how can you adjust the estimate provided by the sample variance?
Divide by the degrees of freedom.
Divide by the square root of n.
Divide by the square root of n-1.
Multiply by n/(n-1).
Multiply by (n-1)/n.

6. For small sample sizes, the sampling distribution of the variance is:
Normally distributed.
Skew negative.
Skew positive.
Standard Error of the Mean
All of the above

7. When we know the variance of a normally distributed population, what distribution can we use to calculate confidence intervals for a population mean.
Binomial
t
z
All of the above are equally good distributions to use to calculate confidence intervals.

8. When we don't know the variance of a normally distributed population, what distribution can we use to calculate confidence intervals for a population mean.
Binomial
t
z
All of the above are equally good distributions to use to calculate confidence intervals.

9. One can use confidence intervals for hypothesis testing.
True
False

10. 95% Confidence Intervals for a population mean:
Are constructed to maximize power.
Are generally preferred over other hypothesis testing measures.
Have a .95 probability of containing the true mean.
Will contain the true mean 95% of the time.
All of the above.

11. For a two-tailed hypothesis about a population mean, the range determined by the critical values is centered around what?
The estimate of the population variance.
The hypothesized mean.
The sample mean.
The population variance.

12. For a two-tailed hypothesis about a population mean, the range for some confidence interval is centered around what?
The estimate of the population variance.
The hypothesized mean.
The sample mean.
The population variance.

13. For a one-tailed hypothesis that the population mean is greater than or equal to some hypothesized value, which tail does the critical value fall in?
The tail above the hypothesized mean.
The tail above the sample mean.
The tail below the hypothesized mean.
The tail below the sample mean.

14. Imagine you were going to create a 'one tailed' confidence interval for hypothesis in the previous question. Which tail does the non-infinite confidence limit fall in?
The tail above the hypothesized mean.
The tail above the sample mean.
The tail below the hypothesized mean.
The tail below the sample mean.

15. When people report confidence intervals, why do they typically report only the 'two-tailed' version of the confidence interval (i.e. confidence intervals without an infinite value).
The 'two-tailed' version creates the largest range.
The 'two-tailed' version creates the smallest range.
The 'two-tailed' version produces the highest confidence.
The 'two-tailed' version produces the lowest confidence.

16. What is the formula for computing the lower confidence limit for the 95 percent confidence interval when the population variance is known? (The numeric subscripts next to the zs and ts represent the z- or t-score that cut off the bottom % of the distribution indicated by the subscript.)

$$\bar{x}+t_{2.5}\frac{\sigma}{\sqrt{n}}$$

$$\bar{x}+t_{2.5}\frac{\hat{\sigma}}{\sqrt{n}}$$

$$\bar{x}+t_{5}\frac{\sigma}{\sqrt{n}}$$

$$\bar{x}+t_{5}\frac{\hat{\sigma}}{\sqrt{n}}$$

$$\bar{x}+t_{95}\frac{\sigma}{\sqrt{n}}$$

$$\bar{x}+t_{95}\frac{\hat{\sigma}}{\sqrt{n}}$$

$$\bar{x}+t_{97.5}\frac{\sigma}{\sqrt{n}}$$

$$\bar{x}+t_{97.5}\frac{\hat{\sigma}}{\sqrt{n}}$$

$$\bar{x}+z_{2.5}\frac{\sigma}{\sqrt{n}}$$

$$\bar{x}+z_{2.5}\frac{\hat{\sigma}}{\sqrt{n}}$$

$$\bar{x}+z_{5}\frac{\sigma}{\sqrt{n}}$$

$$\bar{x}+z_{5}\frac{\hat{\sigma}}{\sqrt{n}}$$

$$\bar{x}+z_{95}\frac{\sigma}{\sqrt{n}}$$

$$\bar{x}+z_{95}\frac{\hat{\sigma}}{\sqrt{n}}$$

$$\bar{x}+z_{97.5}\frac{\sigma}{\sqrt{n}}$$

$$\bar{x}+z_{97.5}\frac{\hat{\sigma}}{\sqrt{n}}$$

17. What is the formula for computing the upper confidence limit for the 95 percent confidence interval when the population variance is not known? (The numeric subscripts next to the zs and ts represent the z- or t-score that cut off the bottom % of the distribution indicated by the subscript.)

$$\bar{x}+t_{2.5}\frac{\sigma}{\sqrt{n}}$$

$$\bar{x}+t_{2.5}\frac{\hat{\sigma}}{\sqrt{n}}$$

$$\bar{x}+t_{5}\frac{\sigma}{\sqrt{n}}$$

$$\bar{x}+t_{5}\frac{\hat{\sigma}}{\sqrt{n}}$$

$$\bar{x}+t_{95}\frac{\sigma}{\sqrt{n}}$$

$$\bar{x}+t_{95}\frac{\hat{\sigma}}{\sqrt{n}}$$

$$\bar{x}+t_{97.5}\frac{\sigma}{\sqrt{n}}$$

$$\bar{x}+t_{97.5}\frac{\hat{\sigma}}{\sqrt{n}}$$

$$\bar{x}+z_{2.5}\frac{\sigma}{\sqrt{n}}$$

$$\bar{x}+z_{2.5}\frac{\hat{\sigma}}{\sqrt{n}}$$

$$\bar{x}+z_{5}\frac{\sigma}{\sqrt{n}}$$

$$\bar{x}+z_{5}\frac{\hat{\sigma}}{\sqrt{n}}$$

$$\bar{x}+z_{95}\frac{\sigma}{\sqrt{n}}$$

$$\bar{x}+z_{95}\frac{\hat{\sigma}}{\sqrt{n}}$$

$$\bar{x}+z_{97.5}\frac{\sigma}{\sqrt{n}}$$

$$\bar{x}+z_{97.5}\frac{\hat{\sigma}}{\sqrt{n}}$$

18. What are degrees of freedom?
The population size.
The sample size.
The number of values that are free to vary before we know the rest given some statistic or statistics.
How much power you have in creating a confidence interval.

19. Which distribution depends on degrees of freedom.
Binomial
t
z
All of the above depend on degrees of freedom.

20. When calculating a mean from 30 observations, what are the degrees of freedom?
0
29
30
31
There is not enough information to tell.