1 A simple random sample of size n is drawn. The sample mean, \( \bar{x} \), is found to be 19.3, and the sample standard deviation, s, is found to be 4.7.**(a)** Construct a 95% confidence interval about \( \mu \) if the sample size, n, is 34.- Lower bound: [ ]- Upper bound: [ ]*(Use ascending order. Round to two decimal places as needed.)***(b)** Construct a 95% confidence interval about \( \mu \) if the sample size, n, is 61.- Lower bound: [ ]- Upper bound: [ ]*(Use ascending order. Round to two decimal places as needed.)***How does increasing the sample size affect the margin of error, E?**- \( \circ \) A. The margin of error decreases.- \( \circ \) B. The margin of error does not change.- \( \circ \) C. The margin of error increases.**(c)** Construct a 99% confidence interval about \( \mu \) if the sample size, n, is 34.- Lower bound: [ ]- Upper bound: [ ]*(Use ascending order. Round to two decimal places as needed.)***Compare the results to those obtained in part (a). How does increasing the level of confidence affect the size of the margin of error, E?**- \( \circ \) A. The margin of error decreases.- \( \circ \) B. The margin of error does not change.- \( \circ \) C. The margin of error increases.**(d)** If the sample size is 14, what conditions must be satisfied to compute the confidence interval?- \( \circ \) A. The sample data must come from a population that is normally distributed with no outliers.- \( \circ \) B. The sample must come from a population that is normally distributed and the sample size must be large.- \( \circ \) C. The sample size must be large and the sample should not have any outliers. **Educational Resource: Understanding the t-Distribution table**The image illustrates a segment of the t-distribution table titled "Table VI: t-Distribution Area in Right Tail." This table is used in statistics to find critical values of the t-distribution based on degrees of freedom (df) and different right tail probability levels.**Diagram Explanation:**- A bell curve graph is shown at the top, representing a t-distribution. The shaded area on the right side of the curve is labeled as "Area in right tail," illustrating the probability of obtaining a value greater than a specific value of \( t \).**Table Explanation:**- **Columns**: The table columns represent different right tail probability 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.- **Rows**: Each row indicates the degrees of freedom (df), ranging from 1 to 16.- **Values**: The table cells contain critical t values corresponding to each df and right tail probability. They are highlighted in sections, suggesting specific confidence levels commonly used in statistical tests.This t-distribution table is crucial for hypothesis testing, enabling researchers to determine thresholds for statistical significance under various sample sizes and confidence levels.

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A simple random sample of size n is drawn. The sample mean, x, is found to be 19.3, and the sample standard deviation, s, is found to be 4.7. E Click the icon to view the table of areas under the t-distribution. ..... (a) Construct a 95% confidence interval about u if the sample size, n, is 34. Lower bound: ; Upper bound: (Use ascending order. Round to two decimal places as needed.) (b) Construct a 95% confidence interval about p if the sample size, n, is 61. Lower bound: O; Upper bound: (Use ascending order. Round to two decimal places as needed.) How does increasing the sample size affect the margin of error, E? O A. The margin of error decreases. O B. The margin of error does not change. C. The margin of error increases. (c) Construct a 99% confidence interval about u if the sample size, n, is 34. Lower bound: ; Upper bound: (Use ascending order. Round to two decimal places as needed.) Compare the results to those obtained in part (a). How does increasing the level of confidence affect the size of the margin of error, E? A. The margin of error decreases. B. The margin of error does not change. C. The margin of error increases.