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Confidence Interval for the mean when s.d. is unknown AND the sample is small

Confidence Interval for the mean when s.d. is unknown AND the sample is small

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Author: Bob Kibler
Description:

At the end of this lesson, you will be able to;

  • Determine when to use a t-score as opposed to a z-score to compute a confidence interval
  • Compute a confidence interval when the standard deviation of the population is unknown and the sample size is small
  • Interpret the meaning of the confidence interval in regard to the population mean
(more)
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Tutorial

Confidence Intervals - t-distribution

t-distribution table

The  highlighted values are the one's used in our lesson.

One Sided 75% 80% 85% 90% 95% 97.50% 99% 99.50% 99.75% 99.90% 99.95%
Two Sided 50% 60% 70% 80% 90% 95% 98% 99% 99.50% 99.80% 99.90%
1 1 1.376 1.963 3.078 6.314 12.71 31.82 63.66 127.3 318.3 636.6
2 0.816 1.061 1.386 1.886 2.92 4.303 6.965 9.925 14.09 22.33 31.6
3 0.765 0.978 1.25 1.638 2.353 3.182 4.541 5.841 7.453 10.21 12.92
4 0.741 0.941 1.19 1.533 2.132 2.776 3.747 4.604 5.598 7.173 8.61
5 0.727 0.92 1.156 1.476 2.015 2.571 3.365 4.032 4.773 5.893 6.869
6 0.718 0.906 1.134 1.44 1.943 2.447 3.143 3.707 4.317 5.208 5.959
7 0.711 0.896 1.119 1.415 1.895 2.365 2.998 3.499 4.029 4.785 5.408
8 0.706 0.889 1.108 1.397 1.86 2.306 2.896 3.355 3.833 4.501 5.041
9 0.703 0.883 1.1 1.383 1.833 2.262 2.821 3.25 3.69 4.297 4.781
10 0.7 0.879 1.093 1.372 1.812 2.228 2.764 3.169 3.581 4.144 4.587
11 0.697 0.876 1.088 1.363 1.796 2.201 2.718 3.106 3.497 4.025 4.437
12 0.695 0.873 1.083 1.356 1.782 2.179 2.681 3.055 3.428 3.93 4.318
13 0.694 0.87 1.079 1.35 1.771 2.16 2.65 3.012 3.372 3.852 4.221
14 0.692 0.868 1.076 1.345 1.761 2.145 2.624 2.977 3.326 3.787 4.14
15 0.691 0.866 1.074 1.341 1.753 2.131 2.602 2.947 3.286 3.733 4.073
16 0.69 0.865 1.071 1.337 1.746 2.12 2.583 2.921 3.252 3.686 4.015
17 0.689 0.863 1.069 1.333 1.74 2.11 2.567 2.898 3.222 3.646 3.965
18 0.688 0.862 1.067 1.33 1.734 2.101 2.552 2.878 3.197 3.61 3.922
19 0.688 0.861 1.066 1.328 1.729 2.093 2.539 2.861 3.174 3.579 3.883
20 0.687 0.86 1.064 1.325 1.725 2.086 2.528 2.845 3.153 3.552 3.85
21 0.686 0.859 1.063 1.323 1.721 2.08 2.518 2.831 3.135 3.527 3.819
22 0.686 0.858 1.061 1.321 1.717 2.074 2.508 2.819 3.119 3.505 3.792
23 0.685 0.858 1.06 1.319 1.714 2.069 2.5 2.807 3.104 3.485 3.767
24 0.685 0.857 1.059 1.318 1.711 2.064 2.492 2.797 3.091 3.467 3.745
25 0.684 0.856 1.058 1.316 1.708 2.06 2.485 2.787 3.078 3.45 3.725
26 0.684 0.856 1.058 1.315 1.706 2.056 2.479 2.779 3.067 3.435 3.707
27 0.684 0.855 1.057 1.314 1.703 2.052 2.473 2.771 3.057 3.421 3.69
28 0.683 0.855 1.056 1.313 1.701 2.048 2.467 2.763 3.047 3.408 3.674
29 0.683 0.854 1.055 1.311 1.699 2.045 2.462 2.756 3.038 3.396 3.659
30 0.683 0.854 1.055 1.31 1.697 2.042 2.457 2.75 3.03 3.385 3.646

 

Notes

Full Screen

CI for mean when s.d. is unknown and the sample size is small

Do I get it? - Answers

1. 58.1 m g

2. d f space equals space n minus 1 space space space space space space space 20 minus 1 equals 19

3. t subscript alpha over 2 end subscript equals 2.093

4. 2.093 open parentheses fraction numerator 4.2 over denominator square root of 20 end fraction close parentheses equals 1.97

5.  58.1 plus-or-minus 1.97 space
56.13 m g space minus space 60.07 m g