4) (10pts) You have been given height data gathered by measuring the heights of

Question

4) (10pts) You have been given height data gathered by measuring the heights of students on a college campus in order to examine two hypotheses: a. Students on the basketball team are typically taller than the general student population. b. The student heights vary the same amount in both groups (populations) Please calculate the following values by hand to the right of the table for each group and then answer the associated questions. (Spts) Heights of students in meters. Random samples from two populations. Student Basketbal team 2.2 1.9 1.8 2.1 body 1.2 2.1 1.7 1.2 1.6 1.7 1.6 2.4 2.4 1.9 2.0 1.7 MEAN MODE MEDIAN What do MEAN, MODE and MEDIAN tell you about a list of values? Be careful to distinguish the differences between them. (1pts) ation What does STANDARD DEVIATION tell you about a set of values? (1pt)

Explanation / Answer

(a)  

mean(x)=sum(x)/n =15.8/10=1.58 and

standard deviation=sd(x)=sqrt(sum(x-mean(x))2/n)=sqrt(0.756/10)=0.275

median is middle observation of the series when arranged in ascending or descending order. here sample size n=10, so there are two observations 5th and 6th are in middle. so average of 5th and 6th will be median i.e. (1.6+1.6)/2=1.6

mode is most frequent observations i.e. value of x which has highest frequency, here 1.2,1.4, 1.6,1.7 each has frequency 2, so this is multi-model problem so mode may be either 1.2 or 1.4 or 1.6 or 1.7.

similar calculation has been done for variable y

(b) standard deviation quantify the amount of variation or dispersion of a set of data values.

(c)No, the two population donot have same height. since the sample means for x and y are different

(d) No , two population donot have same variablity as CV are different

to compare the variability of two series, generally we use coeffiecient of variation (CV)and

CV=100*sd/mean

(e) here we use two sample t-test as sample size is small (less than 30)

if you need details about procedure of t-test application for this example please respond back

following information has been generate using ms-excel

s.n. student body(x) student basketball team (y) 1 1.2 1.7 2 1.2 1.8 3 1.4 1.9 4 1.4 1.9 5 1.6 1.9 6 1.6 2.0 7 1.7 2.1 8 1.7 2.2 9 1.9 2.4 10 2.1 2.4 Mean 1.58 2.03 Median 1.6 1.95 Mode 1.2 or 1.4 or 1.6 or 1.7 1.9 Standard 0.275 0.228 Deviation

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