### Homework #11: Chapters 8 and 9#### 9.4 Section Exercise 9 - 12**Question 26 of 33 (1 point)**In a simple random sample of size \(73\), there were \(35\) individuals in the category of interest.**Part 1 of 4**(a) Compute the sample proportion \(\hat{p}\). Round the answer to at least three decimal places.- The sample proportion is \(\hat{p} = \frac{35}{73} \approx 0.479\).**Alternate Answer:**- \(0.479\)**Part 2 of 4**(b) Are the assumptions for a hypothesis test satisfied? Explain.- **Yes** \(\Large\checkmark\)- **Reason:** The number of individuals in each category is greater than 10.**Part 3 of 4**(c) It is desired to test \(H_0: p = 0.6\) versus \(H_1: p \ne 0.6\). Compute the test statistic. Round the answer to at least two decimal places.- The test statistic is \(Z = -2.10\).**Part 4 of 4**(d) Find the critical value(s) at the 0.01 level. Round the answer(s) to at least three decimal places. If there is more than one critical value, separate them with commas.- **Critical Value(s): \(\pm 2.576\)****Do you reject \(H_0\) at the 0.01 level?**- **Yes** \(\Large\checkmark\)---This format ensures clarity for students accessing the educational content online, providing a structured approach to hypothesis testing and the corresponding calculations in statistical analysis. **Educational Content for Statistical Hypothesis Testing**---**Overview:**This example involves a statistical hypothesis test on the mean weight of one-year-old baby boys, as described in the National Health Statistics Reports. **Problem Statement:**335 one-year-old baby boys were sampled, revealing a mean weight of 25.2 pounds with a standard deviation of 5.3 pounds. A pediatrician claims that the mean weight of one-year-old boys differs from 25 pounds. The test aims to determine if the evidence supports the pediatrician’s claim using a significance level of α = 0.01.**Hypothesis Testing Steps:**### Part 1 of 5**Step 1: State the Hypotheses**- Null Hypothesis (H₀): μ = 25- Alternative Hypothesis (H₁): μ ≠ 25This hypothesis test is a **two-tailed** test.### Part 2 of 5**Step 2: Find the Critical Values**Using the significance level α = 0.01, calculate the critical values for the two-tailed test from the t-distribution.- **Critical values:** -2.576, 2.576### Part 3 of 5**Step 3: Compute the Test Statistic**Calculate the test statistic by applying the formula for the t-test. Round the answer to at least three decimal places.---**Graphical Explanation:**Since there are no actual graphs within the text, let's visualize the distribution for a better understanding:1. **Distribution Curve:** - The central line (mean) represents the hypothesized population mean (25 pounds). - The critical values (-2.576 & 2.576) mark the tails of the distribution under the significance level α = 0.01. 2. **Two-Tailed Test:** - The area to the left of -2.576 and the right of 2.576 represents the rejection regions for the null hypothesis.### Conclusion:By following these steps, students can determine if the sample provides sufficient evidence to reject the null hypothesis in favor of the pediatrician’s claim, using a confidence level corresponding to α = 0.01.---**Tools Used:**- Critical Values for Student's t Distribution Table**Note:**For actual calculations and test results, students are encouraged to use statistical software or perform manual calculations as demonstrated above.---

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Description: ### Homework #11: Chapters 8 and 9#### 9.4 Section Exercise 9 - 12**Question 26 of 33 (1 point)**In a simple random sample of size \(73\), there were \(35\) individuals in the category of interest.**Part 1 of 4**(a) Compute the sample proportion \(\

In the 1st question, we are testing a sample proportion by using a left-tailed z-test and it is…

Math

Statistics

In a simple random sample of size 73, there were 35 individuals in the category of interest. Part 1 of 4 (a) Compute the sample proportion p. Round the answer to at least three decimal places. The sample proportion is 479 Alternate Answer: 0.479 Part 2 of 4 (b) Are the assumptions for a hypothesis test satisfied? Explain. Yes the number of individuals in each category is greater than V 10. Part 3 of 4 (c) It is desired to test H:p-0.6 versus H, :p<06. Compute the test statistic z. Round the answer to at least two decimal places. The test statistic is -2.10 Part: 3 / 4 Part 4 of 4 (d) Find the critical value(s) at the 0.01 level. Round the answer(s) to at least three decimal places. If there is more than one critical value, separate them with commas. Critical value(s):|| Do you reject H, at the 0.01 level? CYes C No

In a simple random sample of size 73, there were 35 individuals in the category of interest. Part 1 of 4 (a) Compute the sample proportion p. Round the answer to at least three decimal places. The sample proportion is 479 Alternate Answer: 0.479 Part 2 of 4 (b) Are the assumptions for a hypothesis test satisfied? Explain. Yes the number of individuals in each category is greater than V 10. Part 3 of 4 (c) It is desired to test H:p-0.6 versus H, :p<06. Compute the test statistic z. Round the answer to at least two decimal places. The test statistic is -2.10 Part: 3 / 4 Part 4 of 4 (d) Find the critical value(s) at the 0.01 level. Round the answer(s) to at least three decimal places. If there is more than one critical value, separate them with commas. Critical value(s):|| Do you reject H, at the 0.01 level? CYes C No

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Up-County Associates is hired to estimate the proportion of county households that own three or more automobiles. They conducted their survey using a simple random sample of 250 randomly selected households and found that 23% of those households owned three or more automobiles. (a) Is the proportion, 23%, a parameter or a statistic? Explain. (b) If Up-County Associates were to continually choose simple random samples of 250 randomly selected households, each time recording the proportion of households in the sample owning three or more automobiles, what would be the “shape” of the resulting distribution of all these sample proportions? Explain. (c) Suppose now that survey company Lower-County Polling also conducted a survey to determine the proportion of county households that own three or more automobiles, but they surveyed only 100 randomly selected households. If Lower-County Polling were also to sample over and over again (using simple random samples…
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