An environmentalist wishes to conduct a hypothesis test on the percentage of cars driven in the city that are hybrids. Is it sufficient for him to use a simple random sample of 189 cars if hybrids currently account for 6% of the car sales in the country and he claims that the percentage of hybrids in the city is higher than that

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19-11-2021
Mathematics

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An environmentalist wishes to conduct a hypothesis test on the percentage of cars driven in the city that are hybrids. Is it sufficient for him to use a simple random sample of 189 cars if hybrids currently account for 6% of the car sales in the country and he claims that the percentage of hybrids in the city is higher than that

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joaobezerra joaobezerra · Answer 1 · 2021-11-29T12:22:04+01:00

Using the condition for the hypothesis test of a proportion, it is found that since there are at least 10 successes and 10 failures in the sample, it is sufficient for him to use a simple random sample of 189 cars.

To test an hypothesis involving a proportion p in a sample of size n, it is needed that there are at least 10 successes and 10 failures, that is, these following conditions are needed.

[tex]np \geq 10[/tex]
[tex]n(1 - p) \geq 10[/tex]

In this problem:

6% of the cars are hybrids, hence [tex]p = 0.06[/tex]
Sample of 189 cars, hence [tex]n = 189[/tex].

Then:

[tex]np = 189(0.06) = 11.34 \geq 10[/tex]

[tex]n(1 - p) = 189(0.94) = 177.66 \geq 10[/tex]

Hence, since there are at least 10 successes and 10 failures in the sample, it is sufficient for him to use a simple random sample of 189 cars.

A similar problem is given at https://brainly.com/question/24261244