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(c) Construct and interpret a 95% confidence interval for the mean age at which a baby first crawls. Select the correct choice and fill in the answer boxes to complete your choice. (Round to one decimal place as needed.)

(c) Construct and interpret a 95% confidence interval for the mean age at which a baby first crawls. Select the correct choice and fill in the answer boxes to complete your choice. (Round to one decimal place as needed.)

MATLAB: An Introduction with Applications
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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**5. The data shown to the right represent the age (in weeks) at which babies first crawl, based on a survey of 12 mothers. Complete parts (a) through (c) below.** **Data:** 52, 30, 44, 35, 47, 37, 56, 26, 52, 47, 28, 28 **Provided Links:** - Critical t-values table - Standard normal distribution table (Page 1 & 2) **(a) Draw a normal probability plot to determine if it is reasonable to conclude the data come from a population that is normally distributed. Choose the correct answer below.** Diagram A and Diagram B show plots with "Expected z score" on the y-axis and "Age (in weeks)" on the x-axis. - Diagram A: Shows non-linear plotted values. - Diagram B: Shows approximately linear plotted values. **Is it reasonable to conclude that the data come from a population that is normally distributed?** - ○ A. No, because the plotted values are not linear. - ○ B. No, because there are not enough values to make a determination. - ● C. Yes, because the plotted values are approximately linear. - ○ D. Yes, because the plotted values are not linear. **(b) Draw a boxplot to check for outliers. Choose the correct answer below.** The diagrams show two boxplots with "Age (in weeks)" on the x-axis. - Diagram A: Shows no extreme values. - Diagram B: Shows no extreme values outside the whiskers. **Does the boxplot suggest that there are outliers?** - ● A. No, there are no points that are outside of the 1.5(IQR) boundary. - ○ B. No, there are no points that are greater than the third quartile or less than the first quartile. - ○ C. Yes, there is at least one point that is outside of the 1.5(IQR) boundary. - ○ D. Yes, there is at least one point that is greater than the third quartile or less than the first quartile. **(c) Construct and interpret a 95% confidence interval for the mean age at which a baby first crawls. Select the correct choice and fill in the answer boxes to complete your choice.** **Note:** Round to one decimal place as needed. - ○
Transcribed Image Text:**5. The data shown to the right represent the age (in weeks) at which babies first crawl, based on a survey of 12 mothers. Complete parts (a) through (c) below.** **Data:** 52, 30, 44, 35, 47, 37, 56, 26, 52, 47, 28, 28 **Provided Links:** - Critical t-values table - Standard normal distribution table (Page 1 & 2) **(a) Draw a normal probability plot to determine if it is reasonable to conclude the data come from a population that is normally distributed. Choose the correct answer below.** Diagram A and Diagram B show plots with "Expected z score" on the y-axis and "Age (in weeks)" on the x-axis. - Diagram A: Shows non-linear plotted values. - Diagram B: Shows approximately linear plotted values. **Is it reasonable to conclude that the data come from a population that is normally distributed?** - ○ A. No, because the plotted values are not linear. - ○ B. No, because there are not enough values to make a determination. - ● C. Yes, because the plotted values are approximately linear. - ○ D. Yes, because the plotted values are not linear. **(b) Draw a boxplot to check for outliers. Choose the correct answer below.** The diagrams show two boxplots with "Age (in weeks)" on the x-axis. - Diagram A: Shows no extreme values. - Diagram B: Shows no extreme values outside the whiskers. **Does the boxplot suggest that there are outliers?** - ● A. No, there are no points that are outside of the 1.5(IQR) boundary. - ○ B. No, there are no points that are greater than the third quartile or less than the first quartile. - ○ C. Yes, there is at least one point that is outside of the 1.5(IQR) boundary. - ○ D. Yes, there is at least one point that is greater than the third quartile or less than the first quartile. **(c) Construct and interpret a 95% confidence interval for the mean age at which a baby first crawls. Select the correct choice and fill in the answer boxes to complete your choice.** **Note:** Round to one decimal place as needed. - ○
# Table of Critical t-Values ## Overview This table provides critical t-values for various degrees of freedom (df) and significance levels (α) in the right tail of a t-distribution. It is commonly used in statistical analyses, especially in hypothesis testing and confidence interval estimation. ## Diagram Explanation - **Graph**: The graph at the top left shows a t-distribution curve, which is bell-shaped and symmetrical like the normal distribution but with heavier tails. The area in the right tail is shaded, indicating the region of interest for critical values, representing the probability α. ## Table Structure ### Columns - **Degrees of Freedom (df)**: These are listed in the first column. They represent the number of independent values or quantities that can vary in the statistical calculation. - **Area in Right Tail (α)**: The remaining columns correspond to various significance levels: 0.25, 0.20, 0.15, 0.10, 0.05, 0.025, 0.02, 0.01, 0.005, 0.0025, 0.001, and 0.0005. These values represent the probability of observing a t-value at least as extreme as the value on the t-distribution. ### Notable Patterns - As the degrees of freedom increase, the critical t-value approaches the critical z-value (normal distribution) for each significance level. - At lower degrees of freedom, the t-values are larger. This reflects the increased uncertainty and variability in smaller sample sizes. ## Table Data Here are the t-values arranged by degrees of freedom (df) and listed for each level of significance (α). Each cell shows the critical t-value that corresponds to the combination of df and α. ### Example values: - For df = 1 and α = 0.05, the critical t-value is 6.314. - For df = 10 and α = 0.01, the critical t-value is 2.764. ### Full Table ``` Degrees of Freedom | 0.25 | 0.20 | 0.15 | 0.10 | 0.05 | 0.025 | 0.02 | 0.01 | 0.005 | 0.0025 | 0.001 | 0.0005 1 | 1.000|
Transcribed Image Text:# Table of Critical t-Values ## Overview This table provides critical t-values for various degrees of freedom (df) and significance levels (α) in the right tail of a t-distribution. It is commonly used in statistical analyses, especially in hypothesis testing and confidence interval estimation. ## Diagram Explanation - **Graph**: The graph at the top left shows a t-distribution curve, which is bell-shaped and symmetrical like the normal distribution but with heavier tails. The area in the right tail is shaded, indicating the region of interest for critical values, representing the probability α. ## Table Structure ### Columns - **Degrees of Freedom (df)**: These are listed in the first column. They represent the number of independent values or quantities that can vary in the statistical calculation. - **Area in Right Tail (α)**: The remaining columns correspond to various significance levels: 0.25, 0.20, 0.15, 0.10, 0.05, 0.025, 0.02, 0.01, 0.005, 0.0025, 0.001, and 0.0005. These values represent the probability of observing a t-value at least as extreme as the value on the t-distribution. ### Notable Patterns - As the degrees of freedom increase, the critical t-value approaches the critical z-value (normal distribution) for each significance level. - At lower degrees of freedom, the t-values are larger. This reflects the increased uncertainty and variability in smaller sample sizes. ## Table Data Here are the t-values arranged by degrees of freedom (df) and listed for each level of significance (α). Each cell shows the critical t-value that corresponds to the combination of df and α. ### Example values: - For df = 1 and α = 0.05, the critical t-value is 6.314. - For df = 10 and α = 0.01, the critical t-value is 2.764. ### Full Table ``` Degrees of Freedom | 0.25 | 0.20 | 0.15 | 0.10 | 0.05 | 0.025 | 0.02 | 0.01 | 0.005 | 0.0025 | 0.001 | 0.0005 1 | 1.000|
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