The CSDATA data set contains the college grade point averages (GPAs) of all 224 students in a university entering class who planned to major in computer science. This is our population. Statistical software packages, like Excel, can take repeated samples to illustrate sampling variability.

a. Choose 25 SRSs of size 20 from this population. (Depending on your version of Excel and Data Analysis package, you may have to make one very large sample of size 500, and then break this sample down into 25 smaller samples. Of course, if you're drawing 500 observations from a population of 225, some students will appear in multiple samples. This isn't a problem. Another option is to use the =RAND() command to create random numbers and then select items from the population using the random number generated by the RAND() command, but this option will take a little longer.) Record the sample mean from each sample and make a histogram of the 25 sample means. (The histogram is a rough approximation of the distribution of the sample mean.)

b. One sign of bias would be that the distribution of sample means was systematically on one side of the true population mean from the data set. Mark the population mean GPA on your histogram of 25 sample means. Is there a clear bias?

c.Find the mean and standard deviation of your 25 sample means. (I.e., find the mean of the sample means, treading each sample as a single "observation," albeit an observation of a sample of 20 students.) We expect the mean of your sample means to be close to the true mean of the population. Is it? We also expect that the standard deviation of the sampling distribution (i.e., standard deviation of your sample means) will be smaller than the standard deviation of the population of 225 students. Is it?

GPA 2.8751 3.2948 3.1347 2.9907 2.9114 4.0000 3.4259 2.6055 3.7785 2.4843 3.1036 3.6987 2.6504 3.3447 2.4286 2.2747 3.1813 3.4381 2.7705 3.5830 3.2845 3.0076 2.4282 3.9318 3.7326 3.6441 3.4046 3.3048 2.7271 2.8174 3.2443 2.9852 3.0306 2.7334 3.3472 3.6309 3.4023 3.3320 3.5572 3.6150 3.2473 2.4335 2.6824 2.8471 2.6142 2.8864 2.6933 3.1962 2.9312 2.4561 3.0874 3.0241 2.4930 2.9928 3.5359 3.4108 3.0315 3.1998 2.3608 3.1173 3.1981 2.8139 4.0000 2.3375 2.5323 2.5122 2.9114 3.4836 2.9211 2.2616 2.5018 3.0513 3.1311 2.9324 3.7269 2.5799 3.4169 2.8891 3.7050 2.9973 2.3386 3.9310 3.1055 3.0351 3.0353 2.9457 2.9983 3.2762 2.5054 3.8952 3.0676 3.8877 3.1631 3.3067 3.2230 3.6862 3.3231 3.5668 3.3184 3.7903 2.9031 2.7975 2.8832 3.2163 2.6160 3.3916 3.2718 3.2557 2.5557 3.4264 2.8497 2.9412 3.1974 3.3895 3.7122 2.8300 3.0160 3.1390 2.6190 3.1824 3.6123 2.4905 3.2289 3.0019 2.6216 2.7189 3.1583 3.3088 3.3301 2.5867 3.6520 2.5492 3.8614 2.7691 3.0557 3.2813 3.5245 2.3771 3.9660 3.1238 2.7522 2.3240 2.6261 3.4228 3.4285 3.4501 3.3694 3.2032 2.6828 3.2894 3.0680 3.6908 2.4668 3.7226 3.0855 2.9902 3.8670 3.3797 2.9569 3.0987 2.7658 3.1880 3.7018 2.5378 3.1207 3.2671 2.7686 3.1685 3.2005 2.5891 3.3155 2.4598 2.5078 3.0404 3.2891 3.3097 3.6319 2.5864 3.2616 3.2668 3.4513 2.4692 2.2765 3.2957 3.0173 3.3651 2.7551 2.8211 2.9015 2.0031 3.4772 3.3989 3.2316 2.9660 2.8600 3.6942 3.1484 2.9071 3.0506 3.2487 3.0027 3.3529 3.3488 2.7835 2.2260 3.7078 3.5532 2.9990 3.0788 3.6568 2.4908 2.8410 2.2331 2.8170 2.7803 3.0143 2.7735 3.6060 3.0440 3.6989 3.6126 3.0972 3.2203 3.3909 3.0934 4 2.003067639