A small sample of 10 units has a mean μ and a standard deviation σ of 1. Find a 98% confidence interval of the mean μ

X - tscore

X = sample mean, s = sample standard deviation, tscore = statistic with (n - 1) Degrees of Freedom and α = 1 - confidence Percentage

Degrees of Freedom = n - 1

Degrees of Freedom = 10 - 1

Degrees of Freedom = 9

α = 1 - Confidence%

α = 1 - 0.98

α = 0.02

α = ½(α)

α = ½(0.02)

α = 0.01

Find t-score for α

tscore

tscore = 2.8214

_{DOF} ^{α} | α _{0.005} | α _{0.01} | α _{0.015} | α _{0.02} | α _{0.025} | α _{0.03} | α _{0.035} | α _{0.04} | α _{0.045} | α _{0.05} |

1 | 63.6559 | 31.821 | 21.2051 | 15.8945 | 12.7062 | 10.5789 | 9.0579 | 7.9158 | 7.0264 | 6.3137 |

2 | 9.925 | 6.9645 | 5.6428 | 4.8487 | 4.3027 | 3.8964 | 3.5782 | 3.3198 | 3.104 | 2.92 |

3 | 5.8408 | 4.5407 | 3.8961 | 3.4819 | 3.1824 | 2.9505 | 2.7626 | 2.6054 | 2.4708 | 2.3534 |

4 | 4.6041 | 3.7469 | 3.2976 | 2.9985 | 2.7765 | 2.6008 | 2.4559 | 2.3329 | 2.2261 | 2.1318 |

5 | 4.0321 | 3.3649 | 3.0029 | 2.7565 | 2.5706 | 2.4216 | 2.2974 | 2.191 | 2.0978 | 2.015 |

6 | 3.7074 | 3.1427 | 2.8289 | 2.6122 | 2.4469 | 2.3133 | 2.2011 | 2.1043 | 2.0192 | 1.9432 |

7 | 3.4995 | 2.9979 | 2.7146 | 2.5168 | 2.3646 | 2.2409 | 2.1365 | 2.046 | 1.9662 | 1.8946 |

8 | 3.3554 | 2.8965 | 2.6338 | 2.449 | 2.306 | 2.1892 | 2.0902 | 2.0042 | 1.928 | 1.8595 |

9 | 3.2498 | 2.8214 | 2.5738 | 2.3984 | 2.2622 | 2.1504 | 2.0554 | 1.9727 | 1.8992 | 1.8331 |

10 | 3.1693 | 2.7638 | 2.5275 | 2.3593 | 2.2281 | 2.1202 | 2.0283 | 1.9481 | 1.8768 | 1.8125 |

11 | 3.1058 | 2.7181 | 2.4907 | 2.3281 | 2.201 | 2.0961 | 2.0067 | 1.9284 | 1.8588 | 1.7959 |

12 | 3.0545 | 2.681 | 2.4607 | 2.3027 | 2.1788 | 2.0764 | 1.9889 | 1.9123 | 1.844 | 1.7823 |

13 | 3.0123 | 2.6503 | 2.4358 | 2.2816 | 2.1604 | 2.06 | 1.9742 | 1.8989 | 1.8317 | 1.7709 |

14 | 2.9768 | 2.6245 | 2.4149 | 2.2638 | 2.1448 | 2.0462 | 1.9617 | 1.8875 | 1.8213 | 1.7613 |

15 | 2.9467 | 2.6025 | 2.397 | 2.2485 | 2.1315 | 2.0343 | 1.9509 | 1.8777 | 1.8123 | 1.7531 |

16 | 2.9208 | 2.5835 | 2.3815 | 2.2354 | 2.1199 | 2.024 | 1.9417 | 1.8693 | 1.8046 | 1.7459 |

17 | 2.8982 | 2.5669 | 2.3681 | 2.2238 | 2.1098 | 2.015 | 1.9335 | 1.8619 | 1.7978 | 1.7396 |

18 | 2.8784 | 2.5524 | 2.3562 | 2.2137 | 2.1009 | 2.0071 | 1.9264 | 1.8553 | 1.7918 | 1.7341 |

19 | 2.8609 | 2.5395 | 2.3457 | 2.2047 | 2.093 | 2 | 1.92 | 1.8495 | 1.7864 | 1.7291 |

20 | 2.8453 | 2.528 | 2.3362 | 2.1967 | 2.086 | 1.9937 | 1.9143 | 1.8443 | 1.7816 | 1.7247 |

21 | 2.8314 | 2.5176 | 2.3278 | 2.1894 | 2.0796 | 1.988 | 1.9092 | 1.8397 | 1.7773 | 1.7207 |

22 | 2.8188 | 2.5083 | 2.3202 | 2.1829 | 2.0739 | 1.9829 | 1.9045 | 1.8354 | 1.7734 | 1.7171 |

23 | 2.8073 | 2.4999 | 2.3132 | 2.177 | 2.0687 | 1.9783 | 1.9003 | 1.8316 | 1.7699 | 1.7139 |

24 | 2.797 | 2.4922 | 2.3069 | 2.1715 | 2.0639 | 1.974 | 1.8965 | 1.8281 | 1.7667 | 1.7109 |

25 | 2.7874 | 2.4851 | 2.3011 | 2.1666 | 2.0595 | 1.9701 | 1.8929 | 1.8248 | 1.7637 | 1.7081 |

26 | 2.7787 | 2.4786 | 2.2958 | 2.162 | 2.0555 | 1.9665 | 1.8897 | 1.8219 | 1.761 | 1.7056 |

27 | 2.7707 | 2.4727 | 2.2909 | 2.1578 | 2.0518 | 1.9632 | 1.8867 | 1.8191 | 1.7585 | 1.7033 |

28 | 2.7633 | 2.4671 | 2.2864 | 2.1539 | 2.0484 | 1.9601 | 1.8839 | 1.8166 | 1.7561 | 1.7011 |

29 | 2.7564 | 2.462 | 2.2822 | 2.1503 | 2.0452 | 1.9573 | 1.8813 | 1.8142 | 1.754 | 1.6991 |

SEM = | σ |

√n |

SEM = | 1 |

√10 |

SEM = | 1 |

3.1622776601684 |

SEM = 0.3162

High End = X + tscore

High End = 5 + 2.8214 x 1/√10

High End = 5 + 2.8214 x 0.31622776601684

High End = 5 + 0.89220501903991

High End = 5.8922

Low End = X - tscore

Low End = 5 - 2.8214 x 1/√10

Low End = 5 - 2.8214 x 0.31622776601684

Low End = 5 - 0.89220501903991

Low End = 4.1078

What this means is if we repeated experiments, the proportion of such intervals that contain μ would be 98%

Free Confidence Interval for the Mean Calculator - Calculates a (90% - 99%) estimation of confidence interval for the mean given a small sample size using the student-t method with (n - 1) degrees of freedom or a large sample size using the normal distribution Z-score (z value) method including Standard Error of the Mean. confidence interval of the mean

This calculator has 5 inputs.

This calculator has 5 inputs.

- confidence interval
- a range of values so defined that there is a specified probability that the value of a parameter lies within it.
- confidence interval for the mean
- a way of estimating the true population mean
- degrees of freedom
- number of values in the final calculation of a statistic that are free to vary
- mean
- A statistical measurement also known as the average
- sample size
- measures the number of individual samples measured or observations used in a survey or experiment.
- standard error of the mean
- measures how far the sample mean (average) of the data is likely to be from the true population mean

SE = σ/√n

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