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It was determined that the percentage of a's in the English language in the 1800s was 9%. A random sample of 1000 letters from a current newspaper contained 66 a's. Test the hypothesis that the proportion of a's has changed in modern times, using the 0.05 level of significance. Treat the newspaper as a random sample of all letters used.

Question

It was determined that the percentage of a's in the English language in the 1800s was 9%. A random sample of 1000 letters from a current newspaper contained 66 a's. Test the hypothesis that the proportion of a's has changed in modern times, using the 0.05 level of significance. Treat the newspaper as a random sample of all letters used. 

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Step 1

It is given that the population proportion; p is 9% (=0.09). In the survey, it is found that 66 of 1000 letters from a current newspaper. Let p be the sample proportion

The null and alternative hypotheses are given below.

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Step 2

The sample proportion, P is calculated below.

66
P =
1000
0.066
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66 P = 1000 0.066

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Step 3

The test statistic is given and...

(Р-р)
P(1- р)
Z
п
(0.066-0.09)
0.09 (1-0.09)
1000
-0.024
0.0090
=-2.67
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(Р-р) P(1- р) Z п (0.066-0.09) 0.09 (1-0.09) 1000 -0.024 0.0090 =-2.67

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