The image contains a table showing the t-distribution values for different degrees of freedom under various levels of significance in the right tail of the distribution. Additionally, there is a graph depicting a t-distribution curve with the shaded area representing the area in the right tail.### Graph Explanation:- **Title**: The graph shows a typical t-distribution curve.- **Shaded Area**: The right tail of the curve is highlighted, indicating the area for which the values in the table are calculated.### Table Details:- **Columns**: The table lists t-values at specific significance levels (0.25, 0.20, 0.15, 0.10, 0.05, 0.025, 0.02, 0.01, 0.005, 0.0025, 0.001, 0.0005) for various degrees of freedom.- **Rows**: Each row corresponds to a different degree of freedom starting from 1 up to 1000 and includes an additional row for infinity.- **Values**: Each cell in the table represents the t-value for the specified degree of freedom and significance level.This table is typically used in statistics to determine critical values for hypothesis testing involving t-distributions, commonly used in estimating population parameters when the sample size is small and the population standard deviation is unknown. The following data represent the pH of rain for a random sample of 12 rain dates. A normal probability plot suggests the data could come from a population that is normally distributed. A boxplot indicates there are no outliers. Complete parts a) through d) below.| 5.05 | 5.72 | 4.99 | 4.80 ||------|------|------|------|| 5.02 | 4.59 | 4.74 | 5.19 || 5.43 | 4.76 | 4.56 | 5.68 |**(a) Determine a point estimate for the population mean.**A point estimate for the population mean is [input box].(Round to two decimal places as needed.)---**Graphical Note:** There is an option to click and view the table of critical t-values, which appears as a button labeled "Table of Critical t-Values."

Answered: (a) Determine a point estimate for the…

(a) Determine a point estimate for the population mean. A point estimate for the population mean is. (Round to two decimal places as needed.)

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

The image contains a table showing the t-distribution values for different degrees of freedom under various levels of significance in the right tail of the distribution. Additionally, there is a graph depicting a t-distribution curve with the shaded area representing the area in the right tail.

### Graph Explanation:
- **Title**: The graph shows a typical t-distribution curve.
- **Shaded Area**: The right tail of the curve is highlighted, indicating the area for which the values in the table are calculated.

### Table Details:
- **Columns**: The table lists t-values at specific significance levels (0.25, 0.20, 0.15, 0.10, 0.05, 0.025, 0.02, 0.01, 0.005, 0.0025, 0.001, 0.0005) for various degrees of freedom.
- **Rows**: Each row corresponds to a different degree of freedom starting from 1 up to 1000 and includes an additional row for infinity.
- **Values**: Each cell in the table represents the t-value for the specified degree of freedom and significance level.

This table is typically used in statistics to determine critical values for hypothesis testing involving t-distributions, commonly used in estimating population parameters when the sample size is small and the population standard deviation is unknown.

The following data represent the pH of rain for a random sample of 12 rain dates. A normal probability plot suggests the data could come from a population that is normally distributed. A boxplot indicates there are no outliers. Complete parts a) through d) below.

| 5.05 | 5.72 | 4.99 | 4.80 |
|------|------|------|------|
| 5.02 | 4.59 | 4.74 | 5.19 |
| 5.43 | 4.76 | 4.56 | 5.68 |

**(a) Determine a point estimate for the population mean.**

A point estimate for the population mean is [input box].

(Round to two decimal places as needed.)

---

**Graphical Note:** There is an option to click and view the table of critical t-values, which appears as a button labeled "Table of Critical t-Values."

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Follow-up Question

(c) Construct and interpret a 99% confidence interval for the mean pH of rainwater. Select the correct
choice below and fill in the answer boxes to complete your choice.
(Use ascending order. Round to two decimal places as needed.)
O A. There is a 99% probability that the true mean pH of rain water is between and
OB. If repeated samples are taken, 99% of them will have a sample pH of rain water between and
and
O C. There is 99% confidence that the population mean pH of rain water is between

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Follow-up Question

The image provides data on the pH of rain from a random sample of 12 rain dates:

- 5.05, 5.72, 4.99, 4.80, 5.02, 4.59, 4.74, 5.19, 5.43, 4.76, 4.56, 5.68

A normal probability plot indicates the data could be from a normally distributed population, with no outliers as shown by a boxplot.

### Tasks:

#### (a) Determine a point estimate for the population mean.
- The point estimate for the population mean is calculated as **5.04** (rounded to two decimal places).

#### (b) Construct and interpret a 95% confidence interval for the mean pH of rainwater.
- Options to choose from:
- **A.** There is a 95% probability that the true mean pH of rain water is between \_\_ and \_\_.
- **B.** There is 95% confidence that the population mean pH of rain water is between \_\_ and \_\_.
- **C.** If repeated samples are taken, 95% of them will have a sample pH of rain water between \_\_ and \_\_.

- To complete this task, one would refer to a table of critical t-values and perform calculations to fill in the confidence interval values as needed, rounding to two decimal places.

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