Introduction
Choose a population distribution (Exponential, Uniform, or Normal) and a sample size, then click the button to generate 10,000 samples and a histogram of the resulting t statistics. Click "Show t curve" to compare this histogram with the t distribution with n-1 degrees of freedom.
Click the "Quiz Me" button to complete the activity.
When a simple random sample (SRS) of size n is drawn from a N(μ, σ) population, the one-sample t statistic has the t distribution with n-1 degrees of freedom. How close is the distribution of the t statistic to the t distribution when the population is not Normal?
This applet allows you to generate thousands of samples with various sizes n from an exponential, uniform, or Normal population distribution. You can then compare the distribution of t statistics against the t distribution used in the one-sample t test.
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Question
1.1
When n = 2, the sampling distribution for the population with the exponential distribution is q8oEs4xwQRwqRTIBQ9YrqHRSmK6YsOST61AmFtD0PGq1ghvs3dDNoslDtyXxpkpF, whereas when n = 50, the sampling distribution for the exponential population is mc7NoJWraBU+Cm/gMHsqD/E23aLhODSejQAN03Cz2nXzfm/YXcD/FyepmZiwM3Tl.
2
Try again.
Incorrect. See above for the correct answers.
Great job.
Question
1.2
gEP3HJnASLrwF20Sm9W0o0oHjd38R05EKAjPJ/rXg8Fuo/KMvvMO6e1HoTQEBtt2/ZgOcn+xdf3LuNW1/ihhm0vBtE6or5w31f5MWHuV4rL3g+WuaYRczsK91/KX/wqJ2SWyw44aBgLl3/0Dm3Xpiqen4pYRtLSdlbafbAOb1i0H5SSTcNLFgEtVGucAED8NQn7Rq7JqWeXP+L/Ny1CU9hhQF59PuDX1X5Kjc4YzEaY/QVv7EBFU/lUQliShf5oS49WgJe8UyJHGf8ckEJFY8DHbX83BNOL1/hDtc86zeuBHsTW8r55OX0FukIMX3EDQW7hP1OnksPAFpCrPfBHtR9v57dfV4R/Wrvc5Dr7andoHNa7YdnKeOPa5YW+T2o9ML7sAoWRH5RKforz7r4UiCzaXtml3bSvqweKbvi6BUW1FS8gcs6PimgFT7+2DcljDx9GuNFoqKH4eIVGXvmLhiAq6SnBLzWGVWWA7+u5l8Iqvf3MMccz4fckIBRPAV579OipH02zJSEu66/ePclk2+DppUiPCFAOOcsvjsbb6+HOWf7vXEFhjSV7R+Ot7S3LXYBBNhc8VUulTtycJBCOjRFUzBqy7h66lTxGW+xtG1H6nzZKVbVNWM7dMzfJtifxtq7yEd/z8imraxtE/oBi2O5z6tWyYgrp07ymL4vuisDN8SwXYLLS0HH+cTsOdG4bV8PVvHpmJlX1HrRIC7aPBIXsr+u82Zfc07ObNgtAuBccZLl535lIXbqy/kLPyRP2w1yzYu9Q6PuJ/INdbFmTFHD8+Zy7++6EIsFelRik2ipF6xVR/P9XUQA==
2
Correct.
Try again.
Incorrect.
Question
1.3
29qPpJBluEGiyLsHhpd3GBeg3xInkFFuMkxenuv8But409MMoKPg3HHifplTk8cdk8SGsEVlClun8wx3vNwvHpz1lsNQPy0QXwghFY/NXi65y6Np6olcztjHu08OLnPt6Nm/8RotjAMka8j9JvyPs/nER2QaJmVOCM/n5mL2hyU7NXFIn3eDndJGveiUUsDWI59w+BcP0DBQkk6hF8G+qpSMIs1uvf4p
The sampling distribution for the exponential population distribution might still be very slightly skewed to the left, but other than this the shapes of the three distributions are virtually identical Normal-shaped curves.
