Let\'s illustrate the idea of a sampling distribution in the case of a very smal

Question

Let's illustrate the idea of a sampling distribution in the case of a very small sample from a very small population. The population is the 10 scholarship players currently on your women's basketball team. For convenience, the 10 players have been labeled with integers 0 to 9. For each player, the total amount of time spent (in minutes) on Facebook during the last week is recorded in the table below. The parameter of interest is the average amount of time on Facebook. The sample is an SRS of size n = 3 drawn from this population of players. Find the mean for the 10 players in the population. This is the population mean, mu. Using R's sample () function, draw a SRS of size 3 from this population (Note: you may sample the same player's time more than once). Write down the three times in your sample and calculate the sample mean, x. This statistic is an estimate of mu. Repeat this process 9 more times using different samples of size 3 generated using R's sampleO function. Make a histogram of the 10 values of x. You are approximating the sampling distribution of X. Is the center of your histogram close to mu? Explain why you would expect it to get closer to it the more times you repeated this sampling process.

Explanation / Answer

mean for 10 players is 108+63+127+210+92+88+161+133+105+168 = 1255 / 10 = 125.5

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