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uysha [10]
3 years ago
12

In the nation of Gondor, the EPA requires that half the new cars sold will meet a certain particulate emission standard a year l

ater. 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
Mathematics
1 answer:
faust18 [17]3 years ago
8 0

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

Step-by-step 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  =  \frac{24}{64}

             \r p  =0.375

Generally the standard error is mathematically evaluated as  

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

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

=>   SE = 0.06525

The  test statistics is evaluated as

        t  =  \frac{ \r p - p }{SE}

        t  =  \frac{ 0.375 - 0.5 }{0.0625}

        t  =  -2

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6 0
2 years ago
Read 2 more answers
Csc (2sin^-1(-12/13))<br> that is 2 times inverse sin of -12/13
german
Answer: -\frac{169}{120}

I'm assuming you mean this:

cosec(2sin^{-1}(\frac{-12}{13}))

Recall what the cosecant function represents. It is the reciprocal of a sine function, and is often written in this form:

\frac{1}{sinx}

So, using the sine relationship:

cosec(2sin^{-1}(\frac{-12}{13})) = \frac{1}{sin(2sin^{-1}(\frac{-12}{13}))}

Let u = sin^{-1}(\frac{-12}{13})
cosec(2sin^{-1}(\frac{-12}{13})) = \frac{1}{sin(2u)}
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= -\frac{13}{24} \cdot \frac{1}{\sqrt{\frac{25}{169}}}
= -\frac{13}{24} \cdot \frac{1}{\frac{5}{13}}
= -\frac{13}{24} \cdot \frac{13}{5}
= -\frac{169}{120}
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