Question

In the nation of Gondor, the EPA requires that half the new cars sold will meet a certain particulate emission standard a year later. A sample of 64 one-year-old cars revealed that only 24 met the particulate emission standard. The test statistic to see whether the proportion is below the requirement is

Answer 1

Complete Question

In the nation of Gondor, the EPA requires that half the new cars sold will meet a certain particulate emission standard a year later. A sample of 64 one-year-old cars revealed that only 24 met the particulate emission standard. The test statistic to see whether the proportion is below the requirement is:

A -1.645

B -2.066

C -2.000

D-1.960

Answer:

The correct option is C

Explanation:

From the question we are told that

The population mean is
`p = 0.50`

The sample size is
`n = 64`

The number that met the standard is
`k = 24`

Generally the sample proportion is mathematically evaluated as

`\r p = (24)/(64)`

`\r p =0.375`

Generally the standard error is mathematically evaluated as

`SE = \sqrt{ (p(1- p ))/(n) }`

=>
`SE = \sqrt{ (0.5 (1- 0.5 ))/(64) }`

=>
`SE = 0.06525`

The test statistics is evaluated as

`t = ( \r p - p )/(SE)`

`t = ( 0.375 - 0.5 )/(0.0625)`

`t = -2`