Consider the population described by the probability distribution shown below. The random variable is observed twice with independent observations. | 1,1 1,2 1,3 1,4 2,1 2,2 2,3 2,4 Full data set o p(x) D 0.3 Sample Probability 0.09 0.03 0.06 0.12 0.03 0.01 0.02 0.04 2 0.1 | 3,1 3,2 3,3 3,4 4,1 4,2 4,3 4,4 Probability 0.06 0.02 0.04 0.08 0.12 0.04 0.08 0.16 0.2 Sample 4. 0.4 a. Complete the sampling distribution table. Type the x values in ascending order, 1.5 2 3.5 Probability 0.09 0.28 0.12 (Type exact answers in simplified form.) b. Construct a probability histogram for the sampling distribution of x. Choose the correct probability histogram below. O A. OB. Oc. OD. 03P(x) 02TP (i) Q 04P) Q 04 04 c. What is the probability that x is 2.5 or larger? The probability that the sample mean is 2.5 or larger is (Type an exact answer in simplified form.) d. Would you expect to observe a value of x equal to 2.5 or larger? Explain. Yes, because the probability is not small. O No, because the probability is small.

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.