Answer :
In the given scenario, in order to calculate an 88% confidence interval, the z statistics that fall at each line marking the middle 88% of scores in the distribution would be +/- 1.555 (from the table).
- In a case of seeking 88% confidence interval, the implication is that there is 12% chance that the interval does not contain the true value i.e., α=0.12
- Assuming a two-sided test, it means that there should be 6% chance attributed to each tail of the z statistics (distribution). Thus, zα/2= z0.06.
- This z value at α/2=0.06 is the coordinate of the Z-curve that has 6% of the distribution's area to its right, and thus 94% of the area to its left.
- It is determined by z-value by reverse-lookup in a z-table.
- Find the closest value in the table to 0.9400 as possible, then see what its row and column is.
- From observation, it is seen that 0.9394 and 0.9406 are in the table with z -values of 1.55 and 1.56 respectively.
- We use liner interpolation to find the experimental z-score:
0.9400 is (0.9400-0.9406)/(0.9394-0.9406) = ½ way from 0.9406 to 0.0394 - So, the z-score for 0.9400 is approximately ½ way from 1.56 to 1.55, hence
Z score = 1.56+((1.55-1.56)*1/2 = 1.5550
Hence the z score = 1.5550
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