Mean 36190476 True mean 12 Std dev 28718668 Sample 25 True s

Mean: 3.6190476; True mean; 12, Std. dev.: 2.8718668, Sample: 25, True sample: 2275

Sampling Distribution: Recall that the sampling distribution of means for a nearly normal variable should be Normal, with a mean equal to the population mean, and a standard deviation equal to the population standard deviation divided by the square root of your sample size. Naturally the true population parameters (mean and standard deviation) for your variable is unknown, however you identified a reasonable estimate in the section above. Based on these estimates, give the sampling distribution model that applies to your variable.

Then use this sampling distribution to find the probability of seeing your data (sample mean) or more extreme by chance. Explain every step of your work and include a diagram of the sampling distribution normal curve and your observed sample statistic (use appropriate technology).

Solution

Z= sample mean minus population mean)/SE

Z = [3.6190476 - 12 ] / 2.87 / srqt(25)

Z = -14.6 using tables of normal distribtuion we will find the probability

Probability will be P( z>-14.6) = 1 - 0.00000005 = 0.999999