A manufacturer claims that 40% of households are planning to purchase a new television in the next two years. An investment analyst is skeptical of this claim. In a survey of 1,010 randomly selected American households, only 374 responded that they plan to purchase a TV in the next two years. Is there convincing evidence that less than 40% of U. S. households plan to purchase a TV? What are the appropriate hypotheses for this test?

Question

Mathematics

Madison Sweeney

2 March, 00:34

A manufacturer claims that 40% of households are planning to purchase a new television in the next two years. An investment analyst is skeptical of this claim. In a survey of 1,010 randomly selected American households, only 374 responded that they plan to purchase a TV in the next two years. Is there convincing evidence that less than 40% of U. S. households plan to purchase a TV? What are the appropriate hypotheses for this test?

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Answers (1)

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Beckham · Answer 1

There is convincing evidence that less than 40% of US households plan to purchase television in the next two years.

Null hypothesis H• = 40%

Alternative Hypothesis Hi < 40%

Step-by-step explanation:

Null hypothesis H• = 40%

From the survey, percentage of household that responded that they plan to buy new television in the next two years is given by

= 374/1010 * 100%

= 37%

Therefore,

Alternative Hypothesis Hi<40%

Hence, there is convincing evidence that less than 40% of US households plan to purchase television in the next two years. Since both null and alternative Hypothesis are less than or equal to 40%.