7.34. Using what we know about the height of 15 year old girls (again = 63.8 inc

Question

7.34. Using what we know about the height of 15 year old girls (again = 63.8 inches and = 2.66 inches), imagine a teacher finds the average height of 14 female students in one of her classes to be 62.4 inches.

(a) calculate the mean and standard error of the distribution of mean heights.

(b) Calculate the z statistic for this group.

(c) What percentage of mean heights, based on samples of this size, would we expect to be shorter than this group?

(d) how often do mean heights as extreme or more extreme than this size occur in this population?

(e) how does the result compare to the statistical significance cutoff of 5%?

Explanation / Answer

Using what we know about the height of 15 year old girls (again µ = 63.8 inches and s = 2.66 inches), imagine a teacher finds the average height of 14 female students in one of her classes to be 62.4 inches. (a) calculate the mean and standard error of the distribution of mean height µ = 63.8 inches, SE=(standard deviation/sqrt(n))=2.66/sqrt(14)=0.710914903 (b) Calculate the z statistic for this group. (observed-expected)/SE=-1.4/.71=-1.97183099 (c) What percentage of mean heights, based on samples of this size, would we expect to be shorter than this group? 0.0243144516775648 (d) how often do mean heights as extreme or more extreme than this size occur in this population? 5% of the time. (e) how does the result compare to the statistical significance cutoff of 5% Slightly less. Likely 14 year olds are significantly shorter.

Related Questions

Navigate

• Browse (All)
• Browse 7
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.