Answer:
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 and 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%.