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Based on this scenario, determine whether you would use a z-statistic, t-statistic, neither, or both, to form a 95% confidence interval. Random sample of size n = 23 from a normal distribution with unknown mean population and standard deviation.

a. Z-statistic
b. Both
c. Neither
d. T-statistic

User Lenicliu
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Final answer:

In this scenario, we would use a t-statistic to form a 95% confidence interval.

Step-by-step explanation:

In this scenario, we have a random sample of size n = 23 from a normal distribution with an unknown mean population and standard deviation. Since the population standard deviation is unknown and the sample size is small (n < 30), we would use a t-statistic to form a 95% confidence interval. The t-statistic takes into account the uncertainty introduced by using the sample standard deviation as an estimate of the population standard deviation.

Example: Let's say we have a sample of heights of n = 23 students. We want to estimate the mean height of all students at the school. Since we don't know the population standard deviation, we would use a t-statistic to calculate the 95% confidence interval for the mean height. This interval would provide a range of plausible values for the population mean.

User Glen Scales
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