Question

A student is considering publishing a new magazine aimed directly at owners of Japanese automobiles. He wanted to estimate the fraction of cars in the United States that are made in Japan. The computer output below summarizes the results of a random sample of 50 autos. z-interval for proportion With 90.00% confidence 0.29938661 < p(japan) < 0.46984416 a. Interpret the computer output. b. Explain what "90% confidence" means. c. A politician urging consumers to purchase products manufactured in the United States says, "Half of all cars in the United States are made in Japan." Does your confidence interval support or contradict this statement? Explain.

Answer 1

Check Explanation

Explanation:

a) Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

With p(japan) representing the true population proportion of US automobile that are made in Japan, the computer output 90% confidence

0.29938661 < p(japan) < 0.46984416

mean that p(japan); the true population proportion of US automobile that are made in Japan lies within the range of proportions (0.29938661, 0.46984416) with an assurance level of 90%.

b) 90% confidence mean that the true proportion may or may not be in the given range, but we are 90% certain that it does.

c) The confidence interval contradicts the politician's claim that "Half of all cars in the United States are made in Japan" because the proportion in the politician's claim, (0.50), does not lie within the range of values that our confidence interval says the true population proportion can take on; (0.29938661, 0.46984416).

0.50 lies outside of the confidence interval obtained for the true population proportion of US automobiles that are made in Japan, hence, the confidence interval contradicts the politician's claim.

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