Question

A recent year was randomly picked from 1985 to the present. In that year, there were 2,051 Hispanic students at Cabrillo College out of a total of 12,328 students. At Lake Tahoe College, there were 321 Hispanic students out of a total of 2,441 students. In general, do you think that the percent of Hispanic students at the two colleges is basically the same or different?

a) The percent of Hispanic students at the two colleges is the same.

b) The percent of Hispanic students at the two colleges is different.

c) Both a,b,and c

d) None of the above

Answer 1

The percentages of Hispanic students at Cabrillo College and Lake Tahoe College are 16.63% and 13.15%, respectively, indicating they are different. The hypothesis test further supports the conclusion that the proportions of Hispanic students at these two colleges are not the same.

Step-by-step explanation:

The question is asking to compare the percentages of Hispanic students at Cabrillo College and Lake Tahoe College to see if they are the same or different. To do this, we need to calculate the percentage of Hispanic students at each college and then compare them.

At Cabrillo College, the percentage of Hispanic students is calculated as follows:

• Number of Hispanic students at Cabrillo College: 2,051
• Total number of students at Cabrillo College: 12,328
• Percentage of Hispanic students: (2,051 / 12,328) × 100 = 16.63%

At Lake Tahoe College, the percentage of Hispanic students is calculated as:

• Number of Hispanic students at Lake Tahoe College: 321
• Total number of students at Lake Tahoe College: 2,441
• Percentage of Hispanic students: (321 / 2,441) × 100 = 13.15%

After calculating the percentages, we can see that 16.63% at Cabrillo College is not the same as 13.15% at Lake Tahoe College, indicating that the percentages are different.

The hypothesis test, with an alpha of 0.05 and resulting decision to reject the null hypothesis, suggests that there is sufficient evidence to conclude that the proportions of Hispanic students at these two colleges are indeed different.