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.

By checking the box below, you certify that the answers you will submit here represent your own work.

1. Compared to the normal distribution, the t-distribution has ______ tails for finite sample sizes.
equal sized
larger
smaller

2. Compared to the normal distribution, the t-distribution has ______ mass located close to the mean t for finite sample sizes.
an equal amount of
less
more

3. Compared to the standard normal distribution, the t-distribution has _______ variance for finite sample sizes.
an equal amount of
less
more

4. As the degrees of freedom increase what happens to the shape of the t-distribution.
It approaches the binomial distribution.
It approaches the standard normal distribution.
It becomes bimodal.
It becomes more skew positive.
It becomes more skew negative.

5. The t-distribution is: (select all that apply)
Centered around 0
Normally Distributed
Symmetric
Unimodal

6. t-tests can be used to evaluate what types of hypotheses.
Hypotheses about the difference between two independent means.
Hypotheses about the differences between two means derived from paired observations.
Hypotheses about the value of a single mean.
All of the above.

7. When calculating t-scores for hypotheses like the mean of some population is Y, what is in the denominator.
An estimate of the population standard deviation.
An estimate of the population variance.
An estimate of the standard error of the mean.
An estimate of the variance of the mean.

8. When calculating t-scores for hypotheses like the mean of some population is Y, what is in the denominator.
A constant.
A variable.

9. If the sample size is 4 how many degrees of freedom are there for a t-test investigating hypotheses like the mean of some population is Y?

10. If the sample size is 4 and the biased estimate of the population variance is 12, what is the unbiased estimate of the population variance?

11. If the sample size is 4 and the biased estimate of the population variance is 12, what is the value of the estimate of the standard deviation that should be used when computing the standard error of the mean?

12. If the sample size is 4 and the biased estimate of the population variance is 12, what is the value of the estimate of the estimated standard error of the mean that should be used when calculating t-scores or confidence intervals?

13. If the sample size is 4 and the biased estimate of the population variance is 12, what is the t-score for a sample mean of 6 when the hypothesized mean is 0?

14. The quantile that cuts off the bottom 2.5% of the t-distribution with the correct degrees of freedom for the previous series of questions is -3.182446. What quantile cuts off the bottom 97.5% of the same distribution?

15. If the sample size is 4, the biased estimate of the population variance is 12, the sample mean is 6, the hypothesized mean is equal to 0, and you're using an alpha of .05, what should you do?
Fail to reject the null.
Reject the null.
Not enough information to tell.

16. If you wanted to create a create a 95% confidence interval for the mean in the previous example, what would the upper limit be?

17. If you wanted to create a create a 95% confidence interval for the mean in the previous example, what would the lower limit be?

18. Based on the confidence interval you just calculated, what should you do?
Fail to reject the null.
Reject the null.
Not enough information to tell.

19. If a t-score like the one you observed cut off the bottom 97.1% of the distribution, what would the p-value for your test be?

20. Based on the p-value you just calculated, what should you do?
Fail to reject the null.
Reject the null.
Not enough information to tell.