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

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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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

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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