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 (a) Determine a point estimate for the population mean A point estimate for the population mean is (Round to two decimal places as needed.) (b) Construct and interpret a 95% 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.) A. There is a 95% probability that the true mean pH of rain water is between and OB. There is 95% confidence that the population mean pH of rain water is between and OC. If repeated samples are taken, 95% of them will have a sample pH of rain water between and Y (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) OA. If repeated samples are taken, 99% of them will have a sample pH of rain water between and B. There is a 99% probability that the true mean pH of rain water is between OC. There is 99% confidence that the population mean pH of rain water is between and between and 3** (d) What happens to the interval as the level of confidence is changed? Explain why this is a logical result As the level of confidence increases, the width of the interval This makes sense since the ▼ ▼ 5.30 5.02 5.29 5.72 4.59 4.76 4 4.89 4.74 4.56 4.80 5 19 5.70 D ▼

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**Transcription of Educational Content on pH Data Analysis**

The image provides an analysis task of pH data for rain collected from a random sample of 12 dates. A normal probability plot indicates the data could originate from a normally distributed population. A boxplot confirms there are no outliers. The data values are as follows:

- 5.30, 5.02, 5.29, 5.72, 4.89, 4.59, 4.74, 5.19, 4.80, 5.70, 4.76, 4.56

**Tasks to Complete:**

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

- A point estimate for the population mean is \_\_
  (Round to two decimal places as needed.)

**(b) Construct and interpret a 95% confidence interval for the mean pH of rainwater.**

Select the correct choice and fill in the answer boxes:

- **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 \_\_

**(c) Construct and interpret a 99% confidence interval for the mean pH of rainwater.**

Select the correct choice and fill in the answer boxes:

- **A.** If repeated samples are taken, 99% of them will have a sample pH of rain water between \_\_ and \_\_
- **B.** There is a 99% probability that the true mean pH of rain water is between \_\_ and \_\_
- **C.** There is 99% confidence that the population mean pH of rain water is between \_\_ and \_\_

**(d) What happens to the interval as the level of confidence is changed? Explain why this is a logical result.**

- As the level of confidence increases, the width of the interval [increases/decreases].
  - [This makes sense since the \_\_]

This exercise trains students in statistical concepts such as point estimation and confidence intervals, which are crucial for data analysis and
Transcribed Image Text:**Transcription of Educational Content on pH Data Analysis** The image provides an analysis task of pH data for rain collected from a random sample of 12 dates. A normal probability plot indicates the data could originate from a normally distributed population. A boxplot confirms there are no outliers. The data values are as follows: - 5.30, 5.02, 5.29, 5.72, 4.89, 4.59, 4.74, 5.19, 4.80, 5.70, 4.76, 4.56 **Tasks to Complete:** **(a) Determine a point estimate for the population mean.** - A point estimate for the population mean is \_\_ (Round to two decimal places as needed.) **(b) Construct and interpret a 95% confidence interval for the mean pH of rainwater.** Select the correct choice and fill in the answer boxes: - **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 \_\_ **(c) Construct and interpret a 99% confidence interval for the mean pH of rainwater.** Select the correct choice and fill in the answer boxes: - **A.** If repeated samples are taken, 99% of them will have a sample pH of rain water between \_\_ and \_\_ - **B.** There is a 99% probability that the true mean pH of rain water is between \_\_ and \_\_ - **C.** There is 99% confidence that the population mean pH of rain water is between \_\_ and \_\_ **(d) What happens to the interval as the level of confidence is changed? Explain why this is a logical result.** - As the level of confidence increases, the width of the interval [increases/decreases]. - [This makes sense since the \_\_] This exercise trains students in statistical concepts such as point estimation and confidence intervals, which are crucial for data analysis and
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