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(c) What would you recommend to a researcher who wants to increase the precision of the interval, but does not have access to additional data? A. The researcher could decrease the level of confidence. B. The researcher could increase the sample mean. C. The researcher could decrease the sample standard deviation. D. The researcher could increase the level of confidence.

(c) What would you recommend to a researcher who wants to increase the precision of the interval, but does not have access to additional data? A. The researcher could decrease the level of confidence. B. The researcher could increase the sample mean. C. The researcher could decrease the sample standard deviation. D. The researcher could increase the level of confidence.

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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Question #5 Part C

### t-Distribution Table This t-distribution table provides critical values for the t-distribution used in statistical analysis, particularly for hypothesis testing and confidence intervals. It is organized by degrees of freedom (df) and the area in the right tail of the distribution. #### Table Overview - **Degrees of Freedom**: Located in the first column on the left, ranging from 1 to 1000, and there is an additional row labeled with \( z \). - **Areas in Right Tail**: Each column corresponds to a different tail probability (\( \alpha \)), including 0.25, 0.20, 0.15, 0.10, 0.05, 0.025, 0.02, 0.01, 0.005, 0.0025, 0.001, 0.0005. - **Critical Values**: The body of the table contains the t-values for the corresponding degrees of freedom and tail probabilities. #### Graphical Representation Located above the table is a graph of the t-distribution. It features: - **Curve**: The t-distribution curve, illustrating the probability density function. - **Highlighted Area**: A shaded section labeled "Area in right tail," indicating the tail region relevant to the table’s critical values. ### How to Use the Table 1. **Determine Degrees of Freedom**: Based on your sample size (n), calculate df as \( df = n - 1 \). 2. **Select Tail Probability**: Choose the appropriate tail probability (\( \alpha \)) for your statistical test. 3. **Find Critical Value**: Locate the intersection of your df row and \( \alpha \) column to find the critical t-value. This table assists in determining the critical t-values necessary for conducting t-tests and constructing confidence intervals for means, especially when dealing with smaller sample sizes where the t-distribution is more appropriate than the normal distribution.
Transcribed Image Text:### t-Distribution Table This t-distribution table provides critical values for the t-distribution used in statistical analysis, particularly for hypothesis testing and confidence intervals. It is organized by degrees of freedom (df) and the area in the right tail of the distribution. #### Table Overview - **Degrees of Freedom**: Located in the first column on the left, ranging from 1 to 1000, and there is an additional row labeled with \( z \). - **Areas in Right Tail**: Each column corresponds to a different tail probability (\( \alpha \)), including 0.25, 0.20, 0.15, 0.10, 0.05, 0.025, 0.02, 0.01, 0.005, 0.0025, 0.001, 0.0005. - **Critical Values**: The body of the table contains the t-values for the corresponding degrees of freedom and tail probabilities. #### Graphical Representation Located above the table is a graph of the t-distribution. It features: - **Curve**: The t-distribution curve, illustrating the probability density function. - **Highlighted Area**: A shaded section labeled "Area in right tail," indicating the tail region relevant to the table’s critical values. ### How to Use the Table 1. **Determine Degrees of Freedom**: Based on your sample size (n), calculate df as \( df = n - 1 \). 2. **Select Tail Probability**: Choose the appropriate tail probability (\( \alpha \)) for your statistical test. 3. **Find Critical Value**: Locate the intersection of your df row and \( \alpha \) column to find the critical t-value. This table assists in determining the critical t-values necessary for conducting t-tests and constructing confidence intervals for means, especially when dealing with smaller sample sizes where the t-distribution is more appropriate than the normal distribution.
The accompanying data represent the total travel tax (in dollars) for a 3-day business trip in 8 randomly selected cities. A normal probability plot suggests the data could come from a population that is normally distributed. A boxplot indicates there are no outliers. Data: 67.82, 70.08, 69.71, 83.48, 79.56, 87.13, 100.69, 99.76 **(a) Determine a point estimate for the population mean travel tax.** A point estimate for the population mean travel tax is $83.28. (Round to two decimal places as needed.) **(b) Construct and interpret a 95% confidence interval for the mean tax paid for a three-day business trip.** Select the correct choice below and fill in the answer boxes to complete your choice. B. One can be 95% confident that the mean travel tax for all cities is between $73.02 and $93.54. (Round to two decimal places as needed.) **(c) What would you recommend to a researcher who wants to increase the precision of the interval, but does not have access to additional data?** A. The researcher could decrease the level of confidence. B. The researcher could increase the sample size. C. The researcher could decrease the sample standard deviation. D. The researcher could increase the level of confidence. **Explanation:** For this problem, the correct option would be the researcher could decrease the level of confidence to increase precision, without additional data. Note: The image also contains a table for critical t-values, which is necessary for calculating the confidence interval.
Transcribed Image Text:The accompanying data represent the total travel tax (in dollars) for a 3-day business trip in 8 randomly selected cities. A normal probability plot suggests the data could come from a population that is normally distributed. A boxplot indicates there are no outliers. Data: 67.82, 70.08, 69.71, 83.48, 79.56, 87.13, 100.69, 99.76 **(a) Determine a point estimate for the population mean travel tax.** A point estimate for the population mean travel tax is $83.28. (Round to two decimal places as needed.) **(b) Construct and interpret a 95% confidence interval for the mean tax paid for a three-day business trip.** Select the correct choice below and fill in the answer boxes to complete your choice. B. One can be 95% confident that the mean travel tax for all cities is between $73.02 and $93.54. (Round to two decimal places as needed.) **(c) What would you recommend to a researcher who wants to increase the precision of the interval, but does not have access to additional data?** A. The researcher could decrease the level of confidence. B. The researcher could increase the sample size. C. The researcher could decrease the sample standard deviation. D. The researcher could increase the level of confidence. **Explanation:** For this problem, the correct option would be the researcher could decrease the level of confidence to increase precision, without additional data. Note: The image also contains a table for critical t-values, which is necessary for calculating the confidence interval.
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