A random sample of the closing stock prices in dollars for a company in recent year is listed below. Assume that o is $2.05. Construct the 90% a 99% confidence intervals for the population mean. Interpret the results a compare the widths of the confidence intervals. 20.05 17.49 21.71 22.72 16.95 16.51 20.45 17.97 17.81 16.34 18.73 15.67 15.41 19.13 16.84 15.54 The 90% confidence interval is ($ 17.24,$18.92). (Round to two decimal places as needed.) The 99% confidence interval is ($.$. ound to two do od)

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### Confidence Intervals for Stock Prices

A random sample of the closing stock prices in dollars for a company in a recent year is listed below. Assume that the population standard deviation (σ) is $2.05. Construct the 90% and 99% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals.

#### Stock Prices Sample:
- 20.05, 17.49, 21.71, 22.72, 17.81
- 16.34, 18.73, 15.67, 17.97, 16.95
- 16.51, 20.45, 15.54, 15.41, 19.13
- 16.84

---

#### Calculated Confidence Intervals:

- **90% Confidence Interval:** ($17.24, $18.92)
  - *Rounded to two decimal places as needed.*

- **99% Confidence Interval:** ($__, $__)
  - *Round to two decimal places as needed.*

---

### Explanation

The confidence intervals represent the range within which we expect the true population mean of the stock prices to fall. The 90% confidence interval is narrower than the 99% confidence interval, reflecting less certainty about the range but more precision. As the confidence level increases, the interval widens, incorporating more potential values of the population mean.
Transcribed Image Text:### Confidence Intervals for Stock Prices A random sample of the closing stock prices in dollars for a company in a recent year is listed below. Assume that the population standard deviation (σ) is $2.05. Construct the 90% and 99% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. #### Stock Prices Sample: - 20.05, 17.49, 21.71, 22.72, 17.81 - 16.34, 18.73, 15.67, 17.97, 16.95 - 16.51, 20.45, 15.54, 15.41, 19.13 - 16.84 --- #### Calculated Confidence Intervals: - **90% Confidence Interval:** ($17.24, $18.92) - *Rounded to two decimal places as needed.* - **99% Confidence Interval:** ($__, $__) - *Round to two decimal places as needed.* --- ### Explanation The confidence intervals represent the range within which we expect the true population mean of the stock prices to fall. The 90% confidence interval is narrower than the 99% confidence interval, reflecting less certainty about the range but more precision. As the confidence level increases, the interval widens, incorporating more potential values of the population mean.
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