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A recent Health of Boston report suggests that 14% of female residents suffer from asthma as opposed to 6% of males. Suppose 250 females and 200 males responded to the study. Which of the following is the correct value of the test statistics?Multiple Choice−1.76−2.761.762.76

Question

A recent Health of Boston report suggests that 14% of female residents suffer from asthma as opposed to 6% of males. Suppose 250 females and 200 males responded to the study. Which of the following is the correct value of the test statistics?Multiple Choice−1.76−2.761.762.76

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Solution

To solve this problem, we need to use the formula for the test statistic in comparing two proportions. The formula is:

Z = (p1 - p2) / sqrt [ p * ( 1 - p ) * ( (1/n1) + (1/n2) ) ]

where p1 and p2 are the sample proportions, n1 and n2 are the sample sizes, and p is the pooled sample proportion.

Given in the problem, we have:

p1 = 0.14 (proportion of females with asthma) n1 = 250 (number of females) p2 = 0.06 (proportion of males with asthma) n2 = 200 (number of males)

First, we need to calculate the pooled sample proportion (p). It is calculated as:

p = (p1 * n1 + p2 * n2) / (n1 + n2)

Substituting the given values:

p = (0.14 * 250 + 0.06 * 200) / (250 + 200) p = 0.105

Now, we substitute all the values into the formula for Z:

Z = (0.14 - 0.06) / sqrt [ 0.105 * ( 1 - 0.105 ) * ( (1/250) + (1/200) ) ] Z = 0.08 / sqrt [ 0.105 * 0.895 * ( 0.004 + 0.005 ) ] Z = 0.08 / sqrt [ 0.094025 * 0.009 ] Z = 0.08 / sqrt [ 0.000846225 ] Z = 0.08 / 0.02908679 Z = 2.75

So, the correct value of the test statistic is approximately 2.76.

This problem has been solved

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