A microbiologist is interested in obtaining an estimate of the average level of

Question

A microbiologist is interested in obtaining an estimate of the average level of some enzyme in a certain human population. She takes a sample of 35 individuals, determines the level of the | enzyme in each, and computes a sample mean of Y = 22 M. It is known that the variable of interest has a population standard deviation of 6.5 UM Specify the sample statistic and its sampling distribution to be used: a. Sample Statistic (1 point) b. Sampling Distribution (1 point) i. Uniform Distribution ii. Normal Distribution ii. Chi-Square Distribution iv. Binomial Distribution v. Poisson Distribution

Explanation / Answer

a) Option 2, Z = (Y_bar - )/(/sqrt(n))

The sample size is greater than 30 and the population standard deviation is known, therefore the z statistic is used over the t statistic. The standard error or the standard deviation of the sampling distribution formula is /sqrt(n).

b) Option 2, Normal distribution.

This is derived from the central limit theorem.
The Central Limit Theorem states that the sampling distribution of the sampling means approaches a normal distribution as the sample size gets larger — no matter what the shape of the population distribution. This fact holds especially true for sample sizes over 30.

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