A publisher reports that 55% of their readers own a particular make of car. a marketing executive wants to test the claim that the percentage is actually different from the reported percentage. a random sample of 200 found that 46% of the readers owned a particular make of car. is there sufficient evidence at the 0.02 level to support the executive's claim?

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19-07-2022
Business

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A publisher reports that 55% of their readers own a particular make of car. a marketing executive wants to test the claim that the percentage is actually different from the reported percentage. a random sample of 200 found that 46% of the readers owned a particular make of car. is there sufficient evidence at the 0.02 level to support the executive's claim?

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Parrain Parrain · Answer 1 · 2022-07-29T21:26:33+02:00

Based on the percentage of readers who own a particular make of the car and the random sample, we can infer that there is sufficient evidence at a 0.02 level to support the executive claim.

What is the evidence to support the executive's claim?

The hypothesis is:

Null hypothesis : P = 0.55

Alternate hypothesis : P ≠ 0.55

We then need to find the test statistic:

= (Probability found by marketing executive - Probability from publisher) / √( (Probability from publisher x (1 - Probability from publisher))/ number of people sampled

= (0.46 - 0.55) / √(( 0.55 x ( 1 - 0.55)) / 200

= -2.56

Using this z value as the test statistic, perform a two-tailed test to show:

= P( Z < -2.56) + P(Z > 2.56)

= 0.0052 + 0.0052

= 0.0104

The p-value is 0.0104 which is less than the significance level of 0.02. This means that we reject the null hypothesis.

The Marketing executive was correct.

Find out more on the null and alternate hypothesis at https://brainly.com/question/25263462

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