g According to a New York Times/CBS News poll conducted during June 24-28, 2011, 55% of the American adults polled said that owning a home is a very important part of the American Dream (The New York Times, June 30, 2011). Suppose this result was true for the population of all American adults in 2011. In a recent poll of 1810 American adults, 62% said that owning a home is a very important part of the American Dream. Perform a hypothesis test to determine whether it is reasonable to conclude that the percentage of all American adults who currently hold this opinion is higher than 55%. Use a 2% significance level, and use both the p-value and the critical-value approaches.

Question

Kadyn Wu

Mathematics

2 January, 02:07

g According to a New York Times/CBS News poll conducted during June 24-28, 2011, 55% of the American adults polled said that owning a home is a very important part of the American Dream (The New York Times, June 30, 2011). Suppose this result was true for the population of all American adults in 2011. In a recent poll of 1810 American adults, 62% said that owning a home is a very important part of the American Dream. Perform a hypothesis test to determine whether it is reasonable to conclude that the percentage of all American adults who currently hold this opinion is higher than 55%. Use a 2% significance level, and use both the p-value and the critical-value approaches.

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Scott Cantrell · Answer 1

Step-by-step explanation:

We would set up the hypothesis test.

a) For the null hypothesis,

P = 0.55

For the alternative hypothesis,

P > 0.55

Considering the population proportion, probability of success, p = 0.55

q = probability of failure = 1 - p

q = 1 - 0.55 = 0.45

Considering the sample,

Probability of success, P = 0.62

Number of samples, n = 1810

We would determine the test statistic which is the z score

z = (P - p) / √pq/n

z = (0.62 - 0.55) / √ (0.55 * 0.45) / 1810 = 5.98

Since this is a right tailed test, the critical value would be the p value to the right of z = 5.98

p value = 0.00001

Since alpha, 0.02 > than the p value, 0.00001, then we would reject the null hypothesis.

Using the critical value approach, By using the critical region method,

the calculated test statistic is 5.98 for the right tail and - 5.98 for the left tail

Since α = 0.02, the critical value is determined from the normal distribution table.

For the left, α/2 = 0.02/2 = 0.01

The z score for an area to the left of 0.01 is - 2.325

For the right, α/2 = 1 - 0.01 = 0.99

The z score for an area to the right of 0.995 is 2.325

In order to reject the null hypothesis, the test statistic must be smaller than - 2.325 or greater than 2.325

Since - 5.98 2.325, we would reject the null hypothesis.

Therefore, it is reasonable to conclude that the percentage of all American adults who currently hold this opinion is higher than 55%.