Exam 11: Inference for a Normal Population

The critical t-value represented by t_0.025(2),20 is the one appropriate for which combination of critical value and degrees of freedom?

In tables of critical t-values, what value of t would correspond to the location with 95% of the distribution less and 5% of the distribution greater when there are 15 degrees of freedom?

When a one sample t-test rejects the null hypothesis, then the 95% confidence interval of the population mean would typically include the value specified in the null hypothesis.

Consider two t-distributions overlaid on the same figure-one for 18 degrees of freedom and one for 20 degrees of freedom. Which of the following corresponds to the location farthest right (i.e., the largest t-value)?

Which of the following does not describe one of the assumptions used in the one sample t-test?

Consider a data sample consisting of 12 values with a mean of 22 and variance of 1.5. What is the approximate 95% confidence interval for the standard deviation?

Consider a situation in which Jamal measures the resting heart rate of 16 individuals from a population that he thinks (based on published reports) has an average resting heart rate of 72 beats per minute. His sample has a mean of 75.2 with a standard deviation of 6.2 cm. If he conducts a one-sample t-test of his data, what t-value would he obtain?

If we have a sample of 11 values with a mean of 15.00 and a standard deviation of 1.30, what is the 95% confidence interval?

Calculation of the confidence intervals for variance and standard deviation may be highly prone to error if the population is not normally distributed.

For a sample of 8 values, what are the critical values we would use to calculate the 95% and 99% confidence intervals?

If the 95% confidence interval of the population mean includes the value specified in the null hypothesis, then we expect the P-value of the one-sample t-test to be larger than 0.05.

Consider a sample with 21 values that has sample mean of 8.00 and a standard deviation of 4.00. Does this sample provide sufficient evidence to conclude that the mean of the population it was sampled from differs from 6.00?

Consider an experiment in which Shireen measures 20 Arabidopsis plants in a pasture that an agricultural company claims have an average height of exactly 23 cm. Her plants have a mean of 24.53 cm with a standard deviation of 2.33 cm, however. If she conducts a one-sample t-test of her data, what t-value would she obtain?

To calculate the confidence intervals for variance and standard deviation, we use the t-distribution.

Which region contains the smallest total area?

For a pair of samples with the same sample size, but where the second has a standard deviation twice as large, the 95% confidence interval for the second sample is twice as wide as the first.

Consider a study on the diet of coyotes. The table shown indicates an analysis of the bones found in the stomachs of 26 roadkill coyotes, and the number of species found in each was measured. Previous studies claim that the mean number of species eaten by coyotes (i.e., the number of species expected in the stomach contents) is 3.4 species per coyote. Conduct a one-sample t-test on this data and determine whether this seems to be true. Assume a = 0.5. In your answer, present the following: your calculated t-value, an exact P-value using a computer or a range for the P-value using a table of critical values, and a statement about whether the population mean appears to be 3.4 or not based on the sample. ​ Number of species' bones found in 26 sets of stomach contents from coyotes. Number of bones Frequency 0 0 1 1 2 2 3 6 4 8 5 6 6 2 7 1 8 0 9 0 10 0

If a population is hypothesized to have a mean value of 15, but the 95% confidence interval based of a sample of 14 values is 16 < μ < 24, what is the t-statistic of the corresponding one sample t-test?

Consider a study on the diet of coyotes. The table shown indicates an analysis of the bones found in the stomachs of 40 roadkill coyotes, and the number of species found in each was measured. Previous studies claim that the mean number of species eaten by coyotes (i.e., the number of species expected in the stomach contents) is 4.5 species per coyote. Conduct a one-sample t-test on this data and determine whether this seems to be true. Assume a = 0.5. In your answer, present the following: your calculated t-value, an exact P-value using a computer or a range for the P-value using a table of critical values, and a statement about whether the population mean appears to be 4.5 or not based on the sample. ​ Number of species' bones found in 40 sets of stomach contents from coyotes. Number of bones Frequency 0 0 1 1 2 2 3 4 4 8 5 9 6 9 7 5 8 1 9 1 10 0 ​

Consider a sample with 25 values that has sample mean of 8.00 and a standard deviation of 5.00. Does this sample provide sufficient evidence to conclude that the mean of the population it was sampled from differs from 6.00?