Statistics and the Sample Standard Deviation Order Instructions

Statistics and the  Sample Standard Deviation Sample Answers

The sample standard deviation can be computed from the population standard deviation. In fact, the sample standard deviation is calculated using the following formula:

=

=

= 1.00

Hence, the standard deviation of 100 people is 1.00.

A mode is an ideal measure of central tendency when dealing with nominal data. It is, mostly, used to determine the most common category. However, it has a limitation that it is not unique. For instance, when there are two or more, highest frequencies (Lucy, 2013). Thus, it leaves the researcher with the problem, especially in the situation when there are more categories with high equal frequencies.

Mean = 65, std. dev. = 2

The z-score of a group of 36 with a mean of 66 will be as follows:

First, we need to obtain the sample standard deviation of the 36 people.

=

=

Notably, the μ _sample = μ _population = 65

z-score =

Thus, the z-score of a group of 36 is 3.00 (Lucy, 2013).

The hypothesis tested in this case is:

μ₀ = 100

μ₀ ≠ 100

Notably, this is a two sides hypothesis test.

Mean = 102, n = 25 μ₀ = 100, α = 0.05

The 95% confidence interval is:

C.I =

s.e. =

s.e. = 1

The critical value =  = 1.96.

CI= 102 1.96*1

CI= 102 1.96

CI = (100.04, 103.96)

Since the interval does not contain the claimed mean of 100, there is no sufficient evidence to claim that the mean is 100 (Lucy, 2013).

The critical values at the 95% level of significance is as follows:

=  = 1.96.

Statistics and the  Sample Standard Deviation References

Lucy, D. (2013). Introduction to statistics for forensic scientists. John Wiley & Sons. From https://books.google.com/books?hl=en&lr=&id=WCo9nLhTDzsC&oi=fnd&pg=PT9&dq=introduction+to+statistics&ots=wunSXou94x&sig=-7y17S27TxgNEBeaErQdxBUDYG0