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Patients recovering from a stroke have their grip strengths, measured in each hand to monitor their progress.

81 viewed last edited 2 months ago
Anonymous
0

A certain population of over 150 female patients have grip strengths in their dominant hands with a mean and standard deviation of approximately 32 kg and 5 kg respectively.

Suppose that we take random samples of 5 female patients from the population and calculate \overline{x} as their sample mean grip strength from each group of patients.

What is the shape of the sampling distribution of \overline{x}?



Sangeetha Pulapaka
1

The shape of the sampling distribution is unknown as it is not given. When a population is normally distributed, the sampling distribution of the sample mean \overline{x} will also be normal regardless of sample size.


When a population is not normally distributed, the sampling distribution of the sample mean \overline{x} depends on the sample size. Sample means coming from large samples n≥30 will be normally distributed, but sample means coming from small samples n<30 may not necessarily be normal.


We are not told anything about the shape of the population distribution of grip strengths, and our sample size of 5 adults is small (5 \lt 30), so we do not know what the shape of the sampling distribution of the sample mean \overline{x} will have.


The shape of the sampling distribution of \overline{x} is unknown, we don't have enough information to determine the shape.