Question

In a sample of 1392 mosquitoes trapped in a region, 1173 tested positive for a certain disease. In a sample of 1457 mosquitoes trapped in a different region, 1196 tested positive for the disease. Compute the test statistic for a hypothesis test to compare the population proportions of mosquitoes in the regions that tested positive for the disease. Assume that the conditions for a hypothesis test for the difference between the population proportions are met. Round your answer to two decimal places.

Answer 1

The value
`z = 1.572`

Explanation:

From the question we are told that

The first sample size is
`n_1 = 1392`

The number that test positive in first sample is
`k = 1173`

The second sample size is
`n_2 = 1457`

The number that tested positive in the second sample is
`z = 1196`

The first sample proportion is mathematically represented as

`\r p_1 = (k)/(n_1)`

=>
`\r p_1 = (1173)/( 1392)`

=>
`\r p_1 =0.843`

The second sample proportion is mathematically represented as

`\r p_2 = (z)/(n_2)`

=>
`\r p_2 = (1196)/( 1457)`

=>
`\r p_2 =0.821`

The null hypothesis is
`\r p_1 = \r p_2`

The alternative hypothesis is
`\r p_1 \\e \r p_2`

Generally test statistics is mathematically represented as

`z = \frac{(\r p_1 - \r p_2)}{ \sqrt{(\r p_1 (1-\r p_1 ))/(n_1) + (\r p_1 (1-\r p_1 ))/(n_1) } } }`

`z =  \frac{(0.843 - 0.821)}{ \sqrt{(0.843 (1-0.843 ))/(1392) +  (0.821 (1-0.821 ))/( 1457) } } }`

`z =  1.572`