## Instructions For this homework: 1. Please provide justification for all your answers and code as...

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## Instructions For this homework: 1. Please provide justification for all your answers and code as much as possible. Justification may include plain text and/or mathematical formulae. 2. Include any mathematical formulae you are using for a calculation. Surrounding mathematical expressions by dollar signs makes the math look nicer and lets you use a special syntax (called Latex) that allows for Greek letters, fractions, etc. Note that this is not R code and therefore should not be put in a code chunk. You can put these immediately before the code chunk where you actually do the calculation. 3. Be sure to check the HW guide in the "Assignment" module in Canvas. **Much of this document is written using mathematical notation that may be difficult to read directly from the Rmd file, So it will be helpful to have a copy of the knitted version of this document to read and answer the questions.** ### Some Notation Your solutions to the problems below must include the formula used for each calculation. To get you started, here is some mathematical expressions written in latex that you may find helpful when writing out the math in your answers. You can copy, paste, and edit these expressions as much as needed. 1. ($\bar x$ 2. ($\bar x$ - - 3. $SE(\bar X) $SE (\bar X) $ $\times$ $z_{\alpha/2}$, $\bar x$ + $SE(\bar X) $ $\times$ $z_{\alpha/2}$) = s/\sqrt{n}$ $SE(\bar x)$ $\times$ $t_{n-1,\alpha/2}$, $\bar x$ + $SE(\bar X) $ $\times$ $t_{n-1,\alpha/2}$) \sigma/\sqrt{n}$ or $SE(\bar X) = 4. $n\hat p \geq 10$ and $n(1-\hat p) \geq 10$ 5. ($\hat p$ - 6. $SE(\hat p) $SE(\hat p) $ $\times$ $z_{\alpha/2}$, $\hat p$ + $SE(\hat_p)$ $\times$ $z_{\alpha/2}$) = \sqrt{\frac{\hat p(1-\hat p)}{n}}$ ### Problem 1 10 recently sold houses were randomly selected from Canton, NY. For each house, the sale price was recorded and this data is in the *HomesForSaleCanton.csv* file. Assume the cost of homes in Canton, NY is normally distributed. a) What distribution should be used to determine the quantiles needed to calculate a 99% confidence interval for mean cost of a home in Canton, NY? Why? **Answer**: b) Compute a 99% confidence interval for the average cost of a home in Canton, NY. Interpret this confidence interval in terms of the study. All of the values needed for the confidence interval (including the lower and upper bounds) must be calculated in a code chunk. **Answer**: How would this confidence interval change if the sample mean and sample variance are unchanged, but the sample size is 35? **Answer**: ## Instructions For this homework: 1. Please provide justification for all your answers and code as much as possible. Justification may include plain text and/or mathematical formulae. 2. Include any mathematical formulae you are using for a calculation. Surrounding mathematical expressions by dollar signs makes the math look nicer and lets you use a special syntax (called Latex) that allows for Greek letters, fractions, etc. Note that this is not R code and therefore should not be put in a code chunk. You can put these immediately before the code chunk where you actually do the calculation. 3. Be sure to check the HW guide in the "Assignment" module in Canvas. **Much of this document is written using mathematical notation that may be difficult to read directly from the Rmd file, So it will be helpful to have a copy of the knitted version of this document to read and answer the questions.** ### Some Notation Your solutions to the problems below must include the formula used for each calculation. To get you started, here is some mathematical expressions written in latex that you may find helpful when writing out the math in your answers. You can copy, paste, and edit these expressions as much as needed. 1. ($\bar x$ 2. ($\bar x$ - - 3. $SE(\bar X) $SE (\bar X) $ $\times$ $z_{\alpha/2}$, $\bar x$ + $SE(\bar X) $ $\times$ $z_{\alpha/2}$) = s/\sqrt{n}$ $SE(\bar x)$ $\times$ $t_{n-1,\alpha/2}$, $\bar x$ + $SE(\bar X) $ $\times$ $t_{n-1,\alpha/2}$) \sigma/\sqrt{n}$ or $SE(\bar X) = 4. $n\hat p \geq 10$ and $n(1-\hat p) \geq 10$ 5. ($\hat p$ - 6. $SE(\hat p) $SE(\hat p) $ $\times$ $z_{\alpha/2}$, $\hat p$ + $SE(\hat_p)$ $\times$ $z_{\alpha/2}$) = \sqrt{\frac{\hat p(1-\hat p)}{n}}$ ### Problem 1 10 recently sold houses were randomly selected from Canton, NY. For each house, the sale price was recorded and this data is in the *HomesForSaleCanton.csv* file. Assume the cost of homes in Canton, NY is normally distributed. a) What distribution should be used to determine the quantiles needed to calculate a 99% confidence interval for mean cost of a home in Canton, NY? Why? **Answer**: b) Compute a 99% confidence interval for the average cost of a home in Canton, NY. Interpret this confidence interval in terms of the study. All of the values needed for the confidence interval (including the lower and upper bounds) must be calculated in a code chunk. **Answer**: How would this confidence interval change if the sample mean and sample variance are unchanged, but the sample size is 35? **Answer**: