Question

Ulse tl Example 1: Given that n = 25, σ is unknown, the CL-95%, and the original population is normally distributed, answer questions a-c. (a) Which distribution is used to find the margin of error E? (b) Why? (c) Find the CV of the correct random variable (Z. or t) if possible. Otherwise state "Not Possible Example 2: Given that n= 16,。-5, the CL-99%, and the original population is normally distributed, answer questions a -c. (a) Which distribution is used to find the margin of error E? (b) Why? (c) Find the CV of the correct random variable (Z or t) if possible. Otherwise state "Not possible" Example 3: Given that n-9, σ is unknown, the CL-90%, and the original population is skewed, answer questions a -e. (a) Which distribution is used to find the margin of error E? (b) Why? (c) Find the CV of the correct random variable (Z or t) if possible. Otherwise state "Not possible" Example 4: 20, σ 10.5, the CL-95%, and the original population is skewed. Given that n answer questions a - c. (a) Which distribution is used to find the margin of error E? (b) Why? (e) Find the CV of the correct random variable (Z or t) if possible. Otherwise state "Not possible"

Answer 1

1) a) studentised t distribution is used to find out the margin of error, because the standard deviation of the population is unknown. In such cases we go to t test for testing the significance

Coefficient of vairation CV is the ratio of Standard deviation to mean is not possible as the standard deviation of the population is unknown

2)As the standard deviation of population is known a normal or z-test can be applied in this case

Here again coefficient of variation is not possible to find as the mean of the sample is not given

3) Since the assumptions of a parametric tests are violated , and the sample size is too small to perform a normal test there are many options to perform a test

!) Non parametric test (such as wilcoxon signed rank test )when the assumptions of parametric tests are not met

ii) Transformation of the data especially in the case of skewed distributions a log transformation will do to make the distribution to be approximately normal