In a random sample of 500 handwritten zip code digits, 464 were read correctly by an optical character recognition (OCR) system operated by the U. S. Postal Service (USPS). USPS would like to know whether the rate is at least 90% correct. Required:
Do the data provide evidence that the rate is at least 90% at a 0.05?

z= 2.38

P = 0.008656

Step-by-step explanation:

Here n= 500 and p~= 464/500= 0.928 and q`= 1- 0.928 = 0.072

We formulate our null and alternate hypothesis as

H0 =  0.9 ;       H0 > 0.9

The degree of confidence = 90%

z₀.₀₅ = 1.645 for  α= 0.05

We use the test statistic

z=  x- np/√npq

z= 466-500 *0.9/ √500 * 0.9(1-0.9)

z= 466- 450/ √45

z= 16/6.7082

z= 2.38

As the calculated value of z= 2.38  is greater than α =1.645 so we reject H0.

If H0 is true the P value is calculated as

P = 1- Ф( 2.38)

P = 1-0.991344=0.008656

a line is an defined derm because it

a)contains an infinite number of points b) can be used to create other geometric shapes c)describes something that does not have width or depth d) is a term that does not have a formal definition. a line is an undefined term because it: contains an infinite number of points.

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