Please provide the following information for Problems 11-22....

Please provide the following information for Problems $11-22$. (a) What is the level of significance? State the null and alternate hypotheses. (b) Check Requirements What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. Compute the appropriate sampling distribution value of the sample test statistic. (c) Find (or estimate) the $P$ -value. Sketch the sampling distribution and show the area corresponding to the $P$ -value. (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level $\alpha ?$ (e) Interpret your conclusion in the context of the application. Note: For degrees of freedom $d . f .$ not given in the Student's $t$ table, use the closest $d . f .$ that is smaller. In some situations, this choice of $d . f .$ may increase the $P$ -value by a small amount and therefore produce a slightly more "conservative" answer. Wildlife: Coyotes A random sample of 46 adult coyotes in a region of northern Minnesota showed the average age to be $\bar{x}=2.05$ years, with sample standard deviation $s=0.82$ years (based on information from the book Coyotes: Biology, Behavior and Management by M. Bekoff, Academic Press). However, it is thought that the overall population mean age of coyotes is $\mu=1.75$. Do the sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of $1.75$ years? Use $\alpha=0.01$

Please provide the following information for Problems $11-22$.
(a) What is the level of significance? State the null and alternate hypotheses.
(b) Check Requirements What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. Compute the appropriate sampling distribution value of the sample test statistic.
(c) Find (or estimate) the $P$ -value. Sketch the sampling distribution and show the area corresponding to the $P$ -value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level $\alpha ?$
(e) Interpret your conclusion in the context of the application. Note: For degrees of freedom $d . f .$ not given in the Student's $t$ table, use the closest $d . f .$ that is smaller. In some situations, this choice of $d . f .$ may increase the $P$ -value by a small amount and therefore produce a slightly more "conservative" answer.
Wildlife: Coyotes A random sample of 46 adult coyotes in a region of northern Minnesota showed the average age to be $\bar{x}=2.05$ years, with sample standard deviation $s=0.82$ years (based on information from the book Coyotes: Biology, Behavior and Management by M. Bekoff, Academic Press). However, it is thought that the overall population mean age of coyotes is $\mu=1.75$. Do the sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of $1.75$ years? Use $\alpha=0.01$

Key Concepts

Level_of_Significance

The level of significance (alpha, ?) is a threshold used in hypothesis testing to determine when to reject the null hypothesis. It represents the probability of rejecting the null hypothesis when it is actually true (Type I error). In hypothesis testing, a specific ? value is pre-determined to ensure that the risk of making a Type I error is controlled.

Null_and_Alternate_Hypotheses

The null hypothesis (H?) is a statement of no effect or status quo, and the alternative hypothesis (H?) is what the researcher aims to support, representing a deviation from the status quo. These hypotheses are formulated based on the research question. The decision to reject or fail to reject H? is based on the evidence provided by the sample data in relation to these hypotheses.

Sampling_Distribution

The sampling distribution is the probability distribution of a sample statistic, such as the sample mean, drawn from a population. When the population standard deviation is unknown and the sample size is relatively small or moderate, the t-distribution is used instead of the normal distribution because it accounts for additional uncertainty introduced by estimating the variability from the sample.

Test_Statistic

The test statistic is a standardized value computed from sample data that is used to decide whether to reject the null hypothesis. For tests involving the sample mean with unknown population standard deviation, the t-statistic is calculated by taking the difference between the sample mean and the hypothesized population mean, divided by the estimated standard error. This statistic is then compared to the critical value from the t-distribution.

P-value

The p-value is the probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true. It quantifies the strength of the evidence against the null hypothesis. A small p-value indicates that the observed result is unlikely under H?, leading to rejection of the null hypothesis.

Decision_Rule

The decision rule in hypothesis testing involves comparing the p-value to the significance level (?) or comparing the test statistic to critical values. If the p-value is less than ?, or if the test statistic falls in the critical region, the null hypothesis is rejected, implying that the observed effect is statistically significant.

Interpretation_of_Conclusion

The interpretation of the conclusion involves explaining the statistical decision (reject or fail to reject the null hypothesis) in the context of the research question. It bridges the gap between the statistical result and its practical implications, ensuring that the findings are meaningful and relevant to the specific domain or application.

Transcript

00:02 In this video, we're going to use information about coyotes to determine whether or not we're going to accept or reject our null hypothesis.

00:12 And we are told that we have a sample size of 46.

00:17 The mean of our sample is 2 .05 years.

00:21 This is how long a coyote lives.

00:25 The standard deviation of our sample is 0 .82.

00:30 We know the mean of the population, so that's 1 .0 .8 .2.

00:33 We know the mean of the population.

00:33 And we are told that our significance level is 0 .01.

00:41 And then we're asked to see is the mean actually greater than 1 .75 years.

00:47 So in this particular situation, we need to state the null hypothesis.

00:56 So remember the null, nothing changes.

01:00 And then our alternative hypothesis will be 1 .75.

01:07 And then we need to determine which type of distribution we're going to do.

01:10 Be using and we will use this the student's t distribution because we don't know the standard deviation of the original population what we do know is the standard deviation of the sample so we're going to use the t distribution and then we're asked to actually calculate it so recall our formula for that is x bar minus mu over the standard deviation divided by the square root of n so when i plug those values in 2 .05 minus 1.

01:47 Divided by 0 .82 divided by the square root of 46.

01:53 Plug all those in and i will get a t value of approximately 2 .481.

02:02 Now i can do this with the calculator, but the calculator gives me a different estimate.

02:08 So i'm choosing to do this one by hand because it's not too hard to do this one by hand.

02:13 Now that i know that my t value, my test statistic is 2 .481, now i'm asked to find or estimate p.

02:24 Now, if i use my calculator immediately, i will know what p is.

02:28 But using my table, i need to go to table four.

02:31 I've copied part of it here.

02:33 I know that my degrees of freedom are 41 because remember, degrees of freedom, the sample size minus 1.

02:40 I said 41, i apologize, 45.

02:42 So my degrees of freedom are 45, so i need to come down my chart, find the row with 45 in it, and then my t value is 2 .481, and i can see that that will fall somewhere between these two numbers.

02:59 And now i know it's a one -tailed distribution, so here's my t value of 2 .481, and my p value will be somewhere in there.

03:15 And then i look between these two numbers and i can see that i have between 0 .010 and 0 .005...

Please give Ace some feedback