Question

in a random sample of males, it was found that 29 write with their left hands and 227 do not. in a random sample of females, it was found that 62 write with their left hands and 467 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. (round to two decimal places as needed) identify the p - value. p - value = 0.436 (round to three decimal places as needed) what is the conclusion based on the hypothesis test? the p - value is greater than the significance level of α = 0.05, so fail to reject the null hypothesis. there is not sufficient evidence to support the claim that the rate of left - handedness among males is less than that among females. b. test the claim by constructing an appropriate confidence interval. the 90% confidence interval is - 0.044 < (p₁ - p₂) < 0.036. (round to three decimal places as needed) what is the conclusion based on the confidence interval? because the confidence interval limits include 0, there does not appear to be a significant difference between the rates of left - handedness among males and females. there is not sufficient evidence to support the claim that the rate of left - handedness among males is less than the rate of left - handedness among females? c. based on the results, is the rate of left - handedness among males less than the rate of left - handedness among females? a. it is reasonable to conclude that the rate of left - handedness among males is the same as the rate of left - handedness among females. b. it is not reasonable to conclude that the rate of left - handedness among males is less than the rate of left - handedness among females. c. it is reasonable to conclude that the rate of left - handedness among males is less than the rate of left - handedness among females. d. the assumptions required for the tests are not valid, so the results should not be used for inference.

Explanation:

For part (c), the 90% confidence interval for \( p_1 - p_2 \) is \( -0.044 < (p_1 - p_2) < 0.036 \). Since this interval includes 0, there is no significant difference between the rates of left - handedness among males and females. So we cannot support the claim that the rate of left - handedness among males is less than that among females. Option B states "It is not reasonable to conclude that the rate of left - handedness among males is less than the rate of left - handedness among females" which matches our conclusion.

Answer:

B. It is not reasonable to conclude that the rate of left - handedness among males is less than the rate of left - handedness among females.