Solve the Problem $\sigma _ { \mathrm { x } } = \frac { \sigma } { \sqrt { \mathrm { n } } } \sqrt { \frac { \mathrm { N } - \mathrm { n } } { \mathrm { N } - 1 } }$

question 93

Essay

Solve the problem.
-When sampling without replacement from a finite population of size N, the following formula is used to find
the standard deviation of the population of sample means: $\sigma _ { \mathrm { x } } = \frac { \sigma } { \sqrt { \mathrm { n } } } \sqrt { \frac { \mathrm { N } - \mathrm { n } } { \mathrm { N } - 1 } }$ However, when the sample size n, is smaller than 5% of the population size, N, the finite population correction
factor, $\sqrt { \frac { N - n } { N - 1 } }$ , can be omitted. Explain in your own words why this is reasonable. For N = 200, find the
values of the finite population correction factor when the sample size is 10%, 5%, 3%, 1% of the population,
respectively. What do you notice?

Understand the characteristics and significance of plant structures including strobili, megaphylls, microphylls, sporangia, and gametophytes.

Comprehend the evolution and diversification of vascular and non-vascular plants through geological periods.

Identify and explain the adaptations plants have evolved for life on land, including cuticles, specialized leaf structures, and reproductive strategies.

Distinguish between different types of plant life cycles and the roles of sporophytes and gametophytes within them.

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