Question

102. 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?

Short answer

Subscripts: $1=$Cabrillo College, $2=$ Lake Tahoe College
(a) The null hypothesis: $H_0:p_1=p_2$
(b) The alternate hypothesis: $H_a:p_1\ne p_2$
(c) The random variable is the difference in Hispanic student proportions at Cabrillo College and Lake Tahoe College.
(d) Two proportions are normal.
(e) The test statistic: $4.29$
(f) The $p$-value: $0.00002$
(g) (i) Alpha: $0.05$
(ii) Decision: Reject the null hypothesis.
(iii) Reason for decision: $p$-value $<$ alpha
(iv) As a result:There is enough data to indicate that Cabrillo College and Lake Tahoe College have differing proportions of Hispanic students.

Step-by-step solution

Given information

To determine that the percent of Hispanic students at the two colleges is basically the same or different.

Explanation

Subscripts:$1=$Cabrillo College, $2=$Lake Tahoe College
(a) The null hypothesis is determined as:

$H0:p1=p2$
(b) The alternate hypothesis is determined as:

$H0:p1\ne p2$
(c) The random variable is the difference in Hispanic student proportions at Cabrillo College and Lake Tahoe College.
(d) Two proportions are normal.
(e) Using Minitab's two sample t test option is determined as:

Hence, the test statistics is $4.58$.

Explanation

(f) The $p$-value from the output is determined as $0.00$.
(g) There is no need for a graph.
(i) $\alpha =0.05$
(ii) Decision: reject the null hypothesis.
(iii) Reason for Decision: $p$-value $<\alpha$.
(iv) As a result: There is enough data to indicate that Cabrillo College and Lake Tahoe College have differing proportions of Hispanic students.