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(i) What is the level of significance? State the null and alternate hypotheses. (ii) Check Requirements What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic? Compute the corresponding $z$ or $t$ value as appropriate. (iii) Find (or estimate) the $P$ -value. Sketch the sampling distribution and show the area corresponding to the $P$ -value. (iv) Based on your answers in parts (i)-(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? (v) Interpret your conclusion in the context of the application.Note: For degrees of freedom $d . f$. not 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 a small amount, and therefore produce a slightly more "conservative" answer.Answers may vary due to rounding.wildlife: Fox Rabies A study of fox rabies in southern Germany gave information about different regions and the occurrence of rabies in each region (Reference: B. Sayers et al., "A Pattern Analysis Study of a Wildlife Rabies Epizootic," Medical Informatics 2:11-34). Based on information from this article, a random sample of $n_{1}=16$ locations in region I gave the following information about the number of cases of fox rabies near that location:$x_{1}:$ Region I data $$\begin{array}{rrrrrrrr}1 & 8 & 8 & 8 & 7 & 8 & 8 & 1 \\ 3 & 3 & 3 & 2 & 5 & 1 & 4 & 6\end{array}$$.A second random sample of $n_{2}=15$ locations in region If gave the following information about the number of cases of fox rabies near that location:$x_{2}:$ Region II data $$\begin{array}{llllllll}1 & 1 & 3 & 1 & 4 & 8 & 5 & 4 \\ 4 & 4 & 2 & 2 & 5 & 6 & 9 &\end{array}$$.Use a calculator with sample mean and sample standard deviation keys to verify that $\bar{x}_{1}=4.75$ with 2 in region I and $\bar{x}_{2}=3.93$ with $s_{2} \approx 2.43$ in region II. (a) Does this information indicate that there is a difference (either way) in the mean number of cases of fox rabies between the two regions? Use a $5 \%$ level of significance. (Assume the distribution of rabies cases in both regions is mound-shaped and approximately normal.) (b) Find a $95 \%$ confidence interval for $\mu_{1}-\mu_{2}$. Explain the meaning of the confidence interval in the context of the problem.

Name: Problem 19, Chapter 10: Understandable Statistics Concepts and Methods
Uploaded: 2021-06-29T19:40:56-08:00
Duration: 3 min 27 s
Channel: Jameson Kuper

   (i) What is the level of significance? State the null and alternate hypotheses.
(ii) Check Requirements What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic? Compute the corresponding $z$ or $t$ value as appropriate.
(iii) Find (or estimate) the $P$ -value. Sketch the sampling distribution and show the area corresponding to the $P$ -value.
(iv) Based on your answers in parts (i)-(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a?
(v) Interpret your conclusion in the context of the application.Note: For degrees of freedom $d . f$. not 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 a small amount, and therefore produce a slightly more "conservative" answer.Answers may vary due to rounding.wildlife: Fox Rabies A study of fox rabies in southern Germany gave information about different regions and the occurrence of rabies in each region (Reference: B. Sayers et al., "A Pattern Analysis Study of a Wildlife Rabies Epizootic," Medical Informatics 2:11-34). Based on information from this article, a random sample of $n_{1}=16$ locations in region I gave the following information about the number of cases of fox rabies near that location:$x_{1}:$ Region I data $$\begin{array}{rrrrrrrr}1 & 8 & 8 & 8 & 7 & 8 & 8 & 1 \\
3 & 3 & 3 & 2 & 5 & 1 & 4 & 6\end{array}$$.A second random sample of $n_{2}=15$ locations in region If gave the following information about the number of cases of fox rabies near that location:$x_{2}:$ Region II data $$\begin{array}{llllllll}1 & 1 & 3 & 1 & 4 & 8 & 5 & 4 \\
4 & 4 & 2 & 2 & 5 & 6 & 9 &\end{array}$$.Use a calculator with sample mean and sample standard deviation keys to verify that $\bar{x}_{1}=4.75$ with 2 in region I and $\bar{x}_{2}=3.93$ with $s_{2} \approx 2.43$ in region II.
(a) Does this information indicate that there is a difference (either way) in the mean number of cases of fox rabies between the two regions? Use a $5 \%$ level of significance. (Assume the distribution of rabies cases in both regions is mound-shaped and approximately normal.)
(b) Find a $95 \%$ confidence interval for $\mu_{1}-\mu_{2}$. Explain the meaning of the confidence interval in the context of the problem.

Understandable Statistics Concepts and Methods

Charles Brase,… 12th Edition

Chapter 10, Problem 19

Instant Answer

Solved by Expert Jameson Kuper

06/29/2021

Step 1

The null hypothesis is that there is no difference in the mean number of cases of fox rabies between the two regions ($\mu_{1} = \mu_{2}$). The alternative hypothesis is that there is a difference in the mean number of cases of fox rabies between the two regions Show more…

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(i) What is the level of significance? State the null and alternate hypotheses. (ii) Check Requirements What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic? Compute the corresponding $z$ or $t$ value as appropriate. (iii) Find (or estimate) the $P$ -value. Sketch the sampling distribution and show the area corresponding to the $P$ -value. (iv) Based on your answers in parts (i)-(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? (v) Interpret your conclusion in the context of the application.Note: For degrees of freedom $d . f$. not 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 a small amount, and therefore produce a slightly more "conservative" answer.Answers may vary due to rounding.wildlife: Fox Rabies A study of fox rabies in southern Germany gave information about different regions and the occurrence of rabies in each region (Reference: B. Sayers et al., "A Pattern Analysis Study of a Wildlife Rabies Epizootic," Medical Informatics 2:11-34). Based on information from this article, a random sample of $n_{1}=16$ locations in region I gave the following information about the number of cases of fox rabies near that location:$x_{1}:$ Region I data $$\begin{array}{rrrrrrrr}1 & 8 & 8 & 8 & 7 & 8 & 8 & 1 \\ 3 & 3 & 3 & 2 & 5 & 1 & 4 & 6\end{array}$$.A second random sample of $n_{2}=15$ locations in region If gave the following information about the number of cases of fox rabies near that location:$x_{2}:$ Region II data $$\begin{array}{llllllll}1 & 1 & 3 & 1 & 4 & 8 & 5 & 4 \\ 4 & 4 & 2 & 2 & 5 & 6 & 9 &\end{array}$$.Use a calculator with sample mean and sample standard deviation keys to verify that $\bar{x}_{1}=4.75$ with 2 in region I and $\bar{x}_{2}=3.93$ with $s_{2} \approx 2.43$ in region II. (a) Does this information indicate that there is a difference (either way) in the mean number of cases of fox rabies between the two regions? Use a $5 \%$ level of significance. (Assume the distribution of rabies cases in both regions is mound-shaped and approximately normal.) (b) Find a $95 \%$ confidence interval for $\mu_{1}-\mu_{2}$. Explain the meaning of the confidence interval in the context of the problem.

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00:01 The following is a solution to number 23, and this is about rabies in fox regions.

00:08 And the first part is just to verify that the sample mean for region 1 was 4 .75, and that standard deviation is 2 .82.

00:15 And then the sample mean for the second region is 3 .93, and the standard deviation is 2 .43.

00:22 And they say use a calculator.

00:23 So i'm assuming it's going to be some sort of scientific or graphing calculator.

00:26 So i went ahead and pre -populated it.

00:28 If you go to stat, this is a ti -84.

00:30 If you go to stat, edit, i went ahead and punched in those numbers already into l1, l2, and then you can find these values fairly quickly if you just go to stat and then one bar stats and then do your l1.

00:46 So this is the verification, so x bar is 4 .75, which is what it was, and then s is about 2 .82.

00:53 And then we'll go ahead and verify on the second one if you go to stat, calc, and then it's one bar stats and then second l2 and we calculate that and that's verified so 3 .93 and then 2 .43 for the standard deviation so that's verified that first part using you know some technology so that's how you would use it in the tid4 and the second part of this we actually do a hypothesis test without formally writing everything down so this is a two sample t test since we don't know what the population standard deviation is so just the sample standard deviation.

01:31 So we're going to use a t test and the significance level is 0 .05.

01:36 And what we're going to do, since we already have the data there, let's go ahead and say stat and then test and it's the two sample t test.

01:43 And i'm going to keep it on data here because i already have the data listed into l1, l2.

01:48 And then everything else can stay the same.

01:51 But the alternative, it says that the two regions are just different either way.

01:56 So we don't know which one's bigger, which one's smaller...

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