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Use a t-distribution to answer the question. Assume the sample is a random sample from a distribution that is reason ably normally distributed and we are doing inference for a sample mean. Find endpoints of a t-distribution with 0.025 beyond them in each tail if the sample has size \(n=25\)

Use a t-distribution to answer the question. Assume the sample is a random sample from a distribution that is reason ably normally distributed and we are doing inference for a sample mean. Find the area in a t-distribution above 2.3 if the sample has size \(n=6\).

Use a t-distribution to answer the question. Assume the sample is a random sample from a distribution that is reason ably normally distributed and we are doing inference for a sample mean. Find the area in a t-distribution above 1.5 if the sample has size \(n=8\).

Use the t-distribution to find a confidence interval for a mean \(\mu\) given the relevant sample results. Give the best point estimate for \(\mu,\) the margin of error, and the confidence interval. Assume the results come from a random sample from a population that is approximately normally distributed. A \(99 \%\) confidence interval for \(\mu\) using the sample results \(\bar{x}=88.3, s=32.1,\) and \(n=15\)

Exercise 6.19 discusses the headline "Domestic cats kill many more wild birds in the United States than scientists thought," and estimates the proportion of domestic cats that hunt outside. A separate study \(^{23}\) used KittyCams to record all activity of \(n=55\) domestic cats that hunt outdoors. The video footage showed that the mean number of kills per week for these cats was 2.4 with a standard deviation of \(1.51 .\) Find and interpret a \(99 \%\) confidence interval for the mean number of kills per week by US household cats that hunt outdoors.

Use StatKey or other technology to generate a bootstrap distribution of sample means and find the standard error for that distribution. Compare the result to the standard error given by the Central Limit Theorem, using the sample standard deviation as an estimate of the population standard deviation. Mean commute time in Atlanta, in minutes, using the data in CommuteAtlanta with \(n=500\), \(\bar{x}=29.11,\) and \(s=20.72\)

Use StatKey or other technology to generate a bootstrap distribution of sample means and find the standard error for that distribution. Compare the result to the standard error given by the Central Limit Theorem, using the sample standard deviation as an estimate of the population standard deviation. Mean price of used Mustang cars online (in \$1000s) using the data in MustangPrice with \(n=25\), \(\bar{x}=15.98,\) and \(s=11.11\)

Test \(H_{0}: \mu=15\) vs \(H_{a}: \mu>15\) using the sample results \(\bar{x}=17.2, s=6.4,\) with \(n=40\)

Test \(H_{0}: \mu=120\) vs \(H_{a} * \mu<120\) using the sample results \(\bar{x}=112.3, s=18.4,\) with \(n=100\)

6.122 Be Nice to Pigeons, As They Remember Your Face In a study \(^{30}\) conducted in Paris, France, equal amounts of pigeon feed were spread on the ground in two adjacent locations. A person was present in both sites, with one acting hostile and running at the birds to scare them away and the other acting neutral and just observing. The two people were randomly exchanged between the two sites throughout and the birds quickly learned to avoid the hostile person's site and to eat at the site of the neutral person. At the end of the training session, both people behaved neutrally but the birds continued to remember which one was hostile. In the most interesting part of the experiment, when the two people exchanged coats (orange worn by the hostile one and yellow by the neutral one throughout training), the pigeons were not fooled and continued to recognize and avoid the hostile person. The quantity measured is difference in number of pigeons at the neutral site minus the hostile site. With \(n=32\) measurements, the mean difference in number of pigeons is 3.9 with a standard deviation of 6.8 . Test to see if this provides evidence that the mean difference is greater than zero, meaning the pigeons can recognize faces (and hold a grudge!)