Question

The vast majority of people have hand dominance--they are either
left-handed or right-handed.

In this question we will ignore the very small percentage of the
population who are

ambidextrous (i.e., those who use both hands equally well or
equally badly!).

A researcher believes that men are more likely to be left-handed
than women. To check this she

checked the dominant hand of random samples of 200 men and 200
women, and found 24 men

and 18 women to be left-handed. Let pM and pW be the proportions
of left-handed men and left-

handed women, respectively, in the population.

Construct an appropriate 95% 1-sided confidence interval to
estimate the difference pM –

pW.

[2]

b) Does your answer to part a) support the researcher’s claim
that men are more likely to be

left-handed? Please explain your reasoning briefly.

[1]

c) Confirm your conclusion in part b) by formulating and testing
the hypothesis (at the 5%

significance level) that men are more likely to be left-handed than
women in the population.

Make sure to compute a p-value.

[5]

d) In a different study, a 95% confidence interval for the
proportion of right-handed people in

the general population was constructed. The interval was 0.89 ±
0.04. Using the same

sample, would a 95% confidence interval for the proportion of
left-handed people in the

general population be 0.11 ± 0.04? Please circle your answer
choice.

[1]

True False Can’t tell

e) Explain if the calculations in parts (a) and (c) require any
assumptions on the distribution of

data on left-handedness in the general population.

Answer #1

Let xM and xW denote the proportion of left-handed women in sample

Here xM = 24/200 = 0.12

xW = 18/200 = 0.09

a) 95% 1-sided confidence interval is

(xM-xW) z* sqrt[( xM(1-xM) + xW(1-xW))/n]

where z is 95% one sided z value and n is sample size of men/women

(0.12-0.09) 1.645* sqrt( (0.12*0.88 + 0.09*0.91) / 200)

0.03 1.645*0.031

0.03 0.05

(-0.02, 0.08)

b) No, answer in part a) does not support the researcher's claim as difference in proportion interval contains negative value too.

c) Let Null hypothesis be

Ho : pM = pW

against Ha : pM > pW

Test statisitic is

z = (xM- xW) / sqrt [ (xM(1-xM) + xW(1-xW))/n

= (0.12-0.09) / sqrt( (0.12*0.88 + 0.09*0.91) / 200)

=0.03/0.031

= 0.96

p value of one sided z test corresponding to z=0.96 is 0.168 > 0.05. Hence it is not significant to reject Ho at 5% level

d) Cant tell, we need to more information to calculate the same.

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Do left-handed people live shorter lives than right-handed
people? A study of this question examined a sample of 949 death
records and contacted next of kin to determine handedness. Note
that there are many possible definitions of "left-handed." The
researchers examined the effects of different definitions on the
results of their analysis and found that their conclusions were not
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average, right-handed people have a left foot that is larger than
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right-handed adults. The table below gives the left and right foot
measurements in millimeters (mm). Test the claim at the 0.01
significance level. You may assume the sample of differences comes
from a normally distributed population.
Person
Left
Foot (x)
Right
Foot (y)
difference (d = x − y)...

Foot-Length: It has been claimed that, on
average, right-handed people have a left foot that is larger than
the right foot. Here we test this claim on a sample of 10
right-handed adults. The table below gives the left and right foot
measurements in millimeters (mm). Test the claim at the 0.01
significance level. You may assume the sample of differences comes
from a normally distributed population.
Person
Left
Foot (x)
Right
Foot (y)
difference (d = x − y)...

Foot-Length: It has been claimed that, on
average, right-handed people have a left foot that is larger than
the right foot. Here we test this claim on a sample of 10
right-handed adults. The table below gives the left and right foot
measurements in millimeters (mm). Test the claim at the 0.05
significance level. You may assume the sample of differences comes
from a normally distributed population.
Person
Left
Foot (x)
Right
Foot (y)
difference (d = x − y)...

Foot-Length: It has been claimed that, on
average, right-handed people have a left foot that is larger than
the right foot. Here we test this claim on a sample of 10
right-handed adults. The table below gives the left and right foot
measurements in millimeters (mm). Test the claim at the 0.05
significance level. You may assume the sample of differences comes
from a normally distributed population.
Person
Left
Foot (x)
Right
Foot (y)
difference (d = x − y)...

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