### Free Educational Resources

• > Mathematics
• > Statistics
• > 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

##### Rating:
(0)
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)

Sophia’s self-paced online courses are a great way to save time and money as you earn credits eligible for transfer to many different colleges and universities.*

No credit card required

28 Sophia partners guarantee credit transfer.

281 Institutions have accepted or given pre-approval for credit transfer.

* The American Council on Education's College Credit Recommendation Service (ACE Credit®) has evaluated and recommended college credit for 25 of Sophia’s online courses. Many different colleges and universities consider ACE CREDIT recommendations in determining the applicability to their course and degree programs.

Tutorial

## 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

of

1.

2.

3.

4.

5.