Bethany & Heather's project

Is there a significant difference = in the proportion of left handed people in the world, estimated to be 13%, and TCH= S?

By:

Heather Spe= arman

And Bethany= Masters

Disclaimer

This study was done in an AP Statistics course with relatively small sample sizes. The validity of such studies must always be questioned. Please keep this in mind if you use or report the results of this study.

Ab= stract

Left-handed people are a minority in= this world. Approximately 13 percent of the world’s population is left-handed.<= /o:p>

Is t= he proportion of left-handed people at Tates Creek High School (TCHS) significantly different from the proportion of left-handed people in the world? This study is to compare the proportion of left-handed people = in the world to that of TCHS. To determine this, a one proportion z test= is used with sample size n=3D82 students. This is used to determine whet= her there is a difference in the proportion of left-handed people in the world = and at TCHS.

Methodology<= /u>

This study was designed to find the proportion of left-handed students at Tates Creek High School (TCHS) and compare it to th= at of the world. To find the sample proportion of left-handed students at TCHS, we chose a sample size of 100 students out of 1606 students. To randomize the study we assigned each student a number (1-1606), then used a random integer generator on our calculator to get 100 numbers. Each of the selected people were then found and given the following survey:<= span style=3D'font-size:10.0pt;line-height:200%;font-family:Georgia;mso-bidi-fon= t-family: Tahoma;color:#DDB8E4'>

This survey is for an AP statistics project. Th= e data collected will be used anonymously. Please sign below to give us permission to use your response.

________________________________

Sign Here

Please circle below whether you write with you left or right hand.

Left &nb= sp; Right

= We could not collect data from 18 of the 100 students due to various reasons s= o we had a sample size of 82 people. Our data is as follows:

Left-handed students: 7/82 = =3D 8.5366%

= Right-handed students: 75/82 =3D 91.4634%

This was found with a one proportion z test.

Analysis and Inference

p=3D Proportion of left han= ded people in the world

p=3D Sample proportion of l= eft handed students at TCHS

Hypotheses: &n= bsp; Ho: p=3D.13

&nbs= p; Ha: p≠.13

Assumptions: n∙po≥10 &n= bsp; = ; 82(.13) =3D10.66 Check

&nbs= p; n(1-po)≥10 &= nbsp; 82(1-.13) =3D71.34 Check

&nbs= p; 10n<population &= nbsp; 10(82) =3D820<1606 Check

&= nbsp; &nbs= p; SRS &= nbsp; &nbs= p; Students were randomly selected Check

p =3D 7/82 =3D .08537

z =3D (p-po)/√(p(1-p)/n) =3D (.08573-.13)/ ͩ= 0;(.13(1-.13)/82) =3D -1.20

2∙P(z≤-1.20) = =3D .2294

Because we got a p value of= .2294, our data is not statistically significant at theα=3D.05 level, therefore we fail to reject Ho, that the proportion of= left handed students at TCHS is 13%. If we had had a bigger sample size, the sample proportion would have given more accurate results, which could have led to that sample being statistically significant.