Q. 102 102. A recent year was randomly ... [FREE SOLUTION]

91影视

Introductory Statistics

Barbara Illowsky, Susan Dean

$Math Studyset 91影视 Explanations$ Math

OER 2018 Edition 路 902 pages

ISBN: 9781938168208

Chapter 10: Q. 102 (page 604)

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

Expert verified

Subscripts: $1 =$ Cabrillo College, $2 =$ Lake Tahoe College
(a) The null hypothesis: $H_{0} : p_{1} = p_{2}$
(b) The alternate hypothesis: $H_{a} : p_{1} 鈮� p_{2}$
(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:

$H 0 : p 1 = p 2$
(b) The alternate hypothesis is determined as:

$H 0 : p 1 鈮� p 2$
(c) The random variable is the difference in Hispanic student proportions at Cabrillo College and Lake Tahoe College.
(d) Two proportions are normal.
(e) 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) $伪 = 0.05$
(ii) Decision: reject the null hypothesis.
(iii) Reason for Decision: $p$ -value $< 伪$ .
(iv) As a result: There is enough data to indicate that Cabrillo College and Lake Tahoe College have differing proportions of Hispanic students.