Question

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 1800 American adults, 60% 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.

Round your answers for the observed value of z and the critical value of z to two decimal places, and the p-value to four decimal places.

z_observed =

p-value =  

Critical value =

We can conclude that the percentage of all American adults who currently hold this opinion is .

Answer 1

Given that In a recent poll of 1800 American adults, 60% said that owning a home is a very important part of the American Dream

So Sample proportion = 0.6

We need to 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%

Null Hypothesis H0 : p 0.55

Alternate Hypothesis H1 : p 0.55

Here Null Hypothesised value p0 = 0.55

Sample size n = 1800

Z-observed = ( - p0) / p0 * (1 - p0) / n

= (0.6 - 0.55) / 0.55 * (1 - 0.55) / 1800

= 0.05 / 0.000138

= 0.05 / 0.011726

= 4.264014

Z-observed = 4.264014

The p-value for a z-score of 4.264014 for a right tailed test = 0.00001 from online calculator

p-value = 0.00001

Critical value is the z-score that has an area of 0.02 to its right since the given significance level is 2%

The z-score that has an area of 0.02 to its right = 2.0537

Critical value = 2.0537

Since the z-observed is greater than the critical value, we will reject Null Hypothesis and We can conclude that the percentage of all American adults who currently hold this opinion is higher than 55%