Refer to Exercise 7.17. a. Use the data entry method in your calculator to find the...

Refer to Exercise 7.17.

a. Use the data entry method in your calculator to find the mean and standard deviation of the 50 values of ̅x given in Exercise 7.17, part c.

b. Compare the values calculated in part a to the theoretical mean µ and the theoretical standard deviation for the sampling distribution of ̅x. How close do the values calculated from the 50 measurements come to the theoretical values?

Reference:

A population consists of N = 5 numbers: 1, 3, 5, 6, and 7. It can be shown that the mean and standard deviation for this population are µ= 4.4 and σ = 2.15, respectively.

a. Construct a probability histogram for this population.

b. Use the random number table, Table 10 in Appendix I, to select a random sample of size n = 10 with replacement from the population. Calculate the sample mean, ̅x. Repeat this procedure, calculating the sample mean ̅x for your second sample.

(HINT: Assign the random digits 0 and 1 to the measurement x = 1; assign digits 2 and 3 to the measurement x = 3, and so on.)

c. To simulate the sampling distribution of ̅x, we have selected 50 more samples of size n = 10 with replacement, and have calculated the corresponding sample means. Construct a relative frequency histogram for these 50 values of ̅x. What is the shape of this distribution?