The Z - Score value is 2.58 would be used to estimate a population mean with 99% confidence based upon a sample of size 15.
Z-score:
The Z-score or standard score is obtained by taking the deviation of a value from the mean and dividing by the standard deviation. These are commonly used in z-tests to compute confidence intervals, such as in principal component analysis,when the standard deviation of the population is known. The t-score is used when the population standard deviation is unknown. We have given that,
The confidence level is 99%.
The sample size is 15
With a 99% confidence level, the significance level is given by: α = 1−0.99 = 0.01
This is a two-tailed test and a single tail for the z test. α/2 = 0.01/2 = 0.005
Now, examine the probability 1 − a/2 = 1 − 0.005
= 0.995 in the z-table. We can see that the probability of 0.995 is almost the value of 2.586..
To learn more about Z score, refer:
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