Question

Identify the null and alternative hypothesis(in symbolic and sentence form), test statistic, P-value(or critical values), conclusion about the null hypothesis, and final conclusion that addresses the original claim(Don’t just say Reject the null hypothesis or fail to reject the null hypothesis). If you used the calculator, identify everything mentioned above in addition to which calculator functions and inputs for each field were used.

1. 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, 1013 were males and 799 were females. Do the data show that there are more male children dying of poisoning than female children? Test at the 1% level.

Answer 1

Solution :

Null and alternative hypotheses :

The null and alternative hypotheses are as follows :

i.e. The population proportion of male children dying from poisoning is less than or equal to 0.50.

i.e. The population proportion of male children dying from poisoning is greater than 0.50.

Test statistic :

To test the hypothesis we shall use z-test for single proportion. The test statistic is given as follows :

Where, p̂ is sample proportion, p is hypothesized value of population proportion under H_{​​​​​​0} and n is sample size.

Sample proportion of male children dying from poisoning is given by,

n = 1830, p = 0.50

The value of the test statistic is 4.5817.

P-value :

Since, our test is right-tailed test, therefore we shall obtain right-tailed p-value for the test statistic. The right-tailed p-value for the test statistic is given as follows:

P-value = P(Z > value of the test statistic)

P-value = P(Z > 4.5817)

P-value = 0.0000

The p-value is 0.0000.

Decision :

Significance level = 1% = 0.01

P-value = 0.0000

(0.0000 < 0.01)

Since, p-value is less than the significance level of 1%, therefore we shall reject the null hypothesis (H_{​​​​​​0}) at 1% significance level.

Conclusion :

At 1% significance level there is sufficient evidence to conclude that there are more male children dying of poisoning than female children.

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