Question

An education firm measures the high school dropout rate as the percentage of 16 to 24 year olds who are not enrolled in school and have not yet earned a high school credential. One year, the high school dropout rate was 6.1%. The next year a polling company took a survey of 1000 people between the ages of 16 and 24 and found that 56 of them are high school dropouts. The polling company would like to determine whether the dropout rate has decreased. The value of the test statistic is

Answer 1

The value of the test statistic
`z = -0.6606`

Explanation:

From the question we are told that

The high dropout rate is
`\mu = 6.1`%
`= 0.061`

The sample size is
`n = 1000`

The number of dropouts
`x = 56`

The probability of having a dropout in 1000 people
`\= x = (56)/(1000) = 0.056`

Now setting up Test Hypothesis

Null
`H_o : p = 0.061`

Alternative
`H_a : p < 0.061`

The Test statistics is mathematically represented as

`z = \frac{\= x - p}{\sqrt{(p(1 -p))/(n) } }`

substituting values

`z = \frac{0.056 - 0.061}{\sqrt{(0.061(1 -0.061))/(1000) } }`

`z = -0.6606`