Question

In a random sample of​ males, it was found that 25 write with their left hands and 223 do not. In a random sample of​ females, it was found that 68 write with their left hands and 442 do not. Use a 0.01 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.

(a.) Test the claim using a hypothesis test.

Consider the first sample to be the sample of males and the second sample to be the sample of females. What are the null and alternative hypotheses for the hypothesis​ test?

(b.) Identify the test statistic.

(c.) Identify the​ P-value.

(d.) What is the conclusion based on the hypothesis​ test?

Answer 1

Basic data:

= Sample proportion of men who write left handed = 25/(223+25) = 25/248 = 0.1008

= Sample proportion of women who = 68/(442+68) = 68/510 = 0.1333

= Overall Proportion = (25 + 68) / (248 + 510) = 0.1227

1 - = 0.8773

= 0.01

(a) The Hypothesis:

H0: p1 = p2 : The proportion of men who write left handed is equal to the proportion of women who write left handed.

Ha: p1 < p2 : The proportion of men who write left handed is lesser than the proportion of women who write left handed.

(b) The Test Statistic:

(c) The p Value: The p value (Left Tail) for Z = 0.82, is; p value = 0.0885

(d) The Decision Rule: If p Value is < Alpha, Then Reject H0.

The Decision: Since p value is > (0.01), We Fail to Reject H0..

The Conclusion: There isn't sufficient evidence at the 0.01 level to conclude that the proportion of men who write left handed is lesser than the proportion of women who write left handed.