Question

According to the U.S. Census Bureau, in 2016 33.4% of the adult population in the U.S. had received at least a bachelor's degree. Suppose that a start-up high-tech firm wishes to locate its headquarters in a city that meets several criteria, one of which is that the proportion of adult residents who have received at least a bachelor's degree in the city is higher than it is nationally. A particular city meets all criteria, except that it is not known whether it satisfies the desired educational level requirement. Therefore, the firm commissions a statistical sampling company to take a sample of the adult residents of the city. Of the 476 adults randomly sampled from the city, 180 had at least a bachelor's degree. The firm wants to test if there is sufficient evidence that the city meets the desired educational requirement. The test statistic is

2.04

1.83

none of the answers provided here

2.09

1.98

Answer 1

Solution :

= x / n = 180 / 476 = 0.3782

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.3782 - 0.334 / [(0.334 * 0.666) / 476]

= 2.04

Test statistic = 2.04