Question

In: Statistics and Probability

In a random sample of​ males, it was found that 26 write with their left hands...

In a random sample of​ males, it was found that 26 write with their left hands and 214 do not. In a random sample of​ females, it was found that 66 write with their left hands and 436 do not. Use a 0.05 significance level to test the claim that the rate of​ left-handedness among males is less than that among females. Complete parts​ (a) through​ (c) below.

Solutions

Expert Solution

H0: null Hypothesis: P1 P2

HA: Alternative Hypothesis:P1 < P2

n1= 240

p1 = 26/240 = 0.1083

n2 = 502

p2 = 66/502= 0.1315

The test statistic is given by:

Table of Area Under Standard Normal Curve gives Z = 0.3159

So,

P - value = 0.5 - 0.3159 = 0.1841

Since P - value = 0.1841 is greater than = 0.05, the difference is not significant. Fail to reject null hypothesis.

The data do not support the claim that the rate of left handedness among males is less than that among females.

For =0.05, critical value of Z = - 1.64.

Since calculated value of Z = - 0.3159 is greater than critical value of Z = - 1.64, the difference is not significant. Fail to reject null hypothesis.

The data do not support the claim that the rate of left handedness among males is less than that among females.


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