Question

A child dying from an accidental poisoning is a terrible incident. Is it more likely that a male child will get into poison than a female child? To find this out, data was collected that showed that out of 1830 children between the ages one and four who pass away from poisoning, 1031 were males and 799 were females (Flanagan, Rooney & Griffiths, 2005).

Do the data show that there are more male children dying of poisoning than female children? Test at the 1% level.

(i) Let p1 = proportion of male children dying of poisoning and p2 = proportion of female children dying of poisoning. Which of the following statements correctly defines the null hypothesis HO?

A. p1 + p2 > 0

B. p1 = p2

C. μ1 = μ2

D. p1 + p2 = 0

(ii) Let p1 = proportion of male children dying of poisoning and p2 = proportion of female children dying of poisoning.

Which of the following statements correctly defines the alternate hypothesis HA?

A. p1 – p2 > 0

B. p1 – p2 = 0

C. μ1 = μ2

D. p1 – p2 < 0

(iii) Enter the level of significance α used for this test: Enter in decimal form.

(iv) Determine pˆ1 and pˆ2 (v) Find pooled sample proportion p¯¯} Let pˆPennsylvania = pˆ1 and pˆUtah = pˆ2

(vi) Calculate and enter test statistic Enter value in decimal form rounded to nearest thousandth, (vii) Determine and enter p-value corresponding to test statistic. Enter value in decimal form rounded to nearest thousandth.

(viii) Comparing p-value and α value, which is the correct decision to make for this hypothesis test?

A. Reject Ho

B. Fail to reject Ho

C. Accept Ho

D. Accept HA

(ix) Select the statement that most correctly interprets the result of this test:

A. The result is statistically significant at .01 level of significance. Sufficient evidence exists to support the claim that the proportion of male children dying of poisoning is more than the proportion of female children dying of poisoning.

B. The result is statistically significant at .01 level of significance. There is not enough evidence to support the claim that the proportion of male children dying of poisoning is more than the proportion of female children dying of poisoning.

C. The result is not statistically significant at .01 level of significance. There is not enough evidence to support the claim that the proportion of male children dying of poisoning is more than the proportion of female children dying of poisoning.

D. The result is not statistically significant at .01 level of significance. Sufficient evidence exists to support the claim that the proportion of male children dying of poisoning is more than the proportion of female children dying of poisoning.

Answer 1

(i) The Null hypothesis H₀ is: B. p1 = p2

(ii) The alternate hypothesis H_a is A. p1 – p2 > 0

(iii) The level of significance, alpha = 0.01

(iv) pˆ1 = 1031/1830 = 0.5634

pˆ2 = 799/1830 = 0.4366

(v) The pooled sample proportion p = (p1 * n1 + p2 * n2) / (n1 + n2) = (1031+799) (1830+1830) = 0.5

(vi) Test statistic = (p1 - p2) / SE (Standard error)

SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] } = sqrt{ p * ( 1 - p ) * [2* (1/n)] } = sqrt{ 0.5 * 0.5 * [2/1830) } = 0.01653

Test statistic = (p1 - p2) / 0.01653 = (0.5634 - 0.4366) / 0.01653 = 7.67

(vii) the P-value is the probability that the z-score is less than -7.67 or greater than 7.67

P(z < -7.67) = 0. Also, P(z > 7.67) = 0

So the p-value is almost 0

(viii) Since the P-value (0) is less than the significance level (0.01), we cannot accept the null hypothesis.

The following options are correct:

A. Reject Ho

D. Accept HA

(ix) Select the statement that most correctly interprets the result of this test:

A. The result is statistically significant at .01 level of significance. Sufficient evidence exists to support the claim that the proportion of male children dying of poisoning is more than the proportion of female children dying of poisoning.