The prices of used books at a large college bookstore are normally distributed. If a sample of 23 used books from this store has a mean price of $27.50 with a standard deviation of $6.75, use Table 10.1 to calculate the following for a 95% confidence level about the population mean.a. Degrees of freedomb. The critical value of tc. The margin of errord. The confidence interval for a 95% confidence level ### Table 10.1: Critical t Values#### DescriptionThis table provides t-critical values for different degrees of freedom (df) at a significance level of 0.05 for both one-tailed and two-tailed tests. #### How to Use the Table:- **Degrees of Freedom (df)**: This is typically calculated as the sample size (n) minus 1 (df = n - 1).- **Two-Tailed Test**: If you are conducting a two-tailed test with a 0.05 significance level, locate the critical value under the column labeled "0.05 area in two tails".- **One-Tailed Test**: If you are conducting a one-tailed test with a 0.05 significance level, locate the critical value under the column labeled "0.05 area in one tail".#### Table:| Degrees of Freedom (n – 1) | 0.05 area in two tails | 0.05 area in one tail | Degrees of Freedom (n – 1) | 0.05 area in two tails | 0.05 area in one tail ||---|---|---|---|---|---|| 1 | 12.706 | 6.314 | 28 | 2.048 | 1.701 || 2 | 4.303 | 2.920 | 29 | 2.045 | 1.699 || 3 | 3.182 | 2.353 | 30 | 2.042 | 1.697 || 4 | 2.776 | 2.132 | 31 | 2.040 | 1.696 || 5 | 2.571 | 2.015 | 32 | 2.037 | 1.694 || 6 | 2.447 | 1.943 | 33 | 2.035 | 1.692 || 7 | 2.365 | 1.895 | 34 | 2.032 | 1.691 || 8 | 2.306 | 1.860 | 35 | 2.030 | 1.690 || 9 | 2.262 | 1.833

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Description: The prices of used books at a large college bookstore are normally distributed. If a sample of 23 used books from this store has a mean price of $27.50 with a standard deviation of $6.75, use Table 10.1 to calculate the following for a 95% confidence

From the provided information, Sample size (n) = 23 Sample mean (x̅) = $27.50 Sample standard…

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MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

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The prices of used books at a large college bookstore are normally distributed. If a sample of 23 used books from this store has a mean price of $27.50 with a standard deviation of $6.75, use Table 10.1 to calculate the following for a 95% confidence level about the population mean.

a. Degrees of freedom

b. The critical value of t

c. The margin of error

d. The confidence interval for a 95% confidence level

### Table 10.1: Critical t Values

#### Description
This table provides t-critical values for different degrees of freedom (df) at a significance level of 0.05 for both one-tailed and two-tailed tests.

#### How to Use the Table:
- **Degrees of Freedom (df)**: This is typically calculated as the sample size (n) minus 1 (df = n - 1).
- **Two-Tailed Test**: If you are conducting a two-tailed test with a 0.05 significance level, locate the critical value under the column labeled "0.05 area in two tails".
- **One-Tailed Test**: If you are conducting a one-tailed test with a 0.05 significance level, locate the critical value under the column labeled "0.05 area in one tail".

#### Table:

| Degrees of Freedom (n – 1) | 0.05 area in two tails | 0.05 area in one tail | Degrees of Freedom (n – 1) | 0.05 area in two tails | 0.05 area in one tail |
|---|---|---|---|---|---|
| 1 | 12.706 | 6.314 | 28 | 2.048 | 1.701 |
| 2 | 4.303 | 2.920 | 29 | 2.045 | 1.699 |
| 3 | 3.182 | 2.353 | 30 | 2.042 | 1.697 |
| 4 | 2.776 | 2.132 | 31 | 2.040 | 1.696 |
| 5 | 2.571 | 2.015 | 32 | 2.037 | 1.694 |
| 6 | 2.447 | 1.943 | 33 | 2.035 | 1.692 |
| 7 | 2.365 | 1.895 | 34 | 2.032 | 1.691 |
| 8 | 2.306 | 1.860 | 35 | 2.030 | 1.690 |
| 9 | 2.262 | 1.833

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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