Question

Kelsey Matthau is an advisor for a high school. The high school offers a class for students preparing to take college admissions exams. Kelsey is looking for evidence that the population mean score of students who attend the college admissions class is greater than the population mean score of students who do not attend. Since the school has every student take the exam during school hours, Kelsey has access to the students' scores.

Using information from past years, she assumes that the population standard deviation is 5.42 for the students who attended the class and 6.17 for students who did not attend the class. Without looking at the names of the students, Kelsey randomly selects the college admissions exam scores of students who attended the class and of students who did not attend the class.

The results of the samples are provided in the table below. Explain whether a hypothesis test for the difference between two means of independent samples is appropriate, and if so, determine the null and alternative hypotheses for this hypothesis test. Let μ1 be the population mean exam score for students who attended the class and μ2 be the population mean exam score for students who did not attend the class.

Answer 1

A hypothesis test for the difference between two means of independent samples is appropriate, because

Independent-samples t tests compare scores on the same variable but for two different groups of cases whereas

Paired-samples t tests compare scores on two different variables but for the same group of cases

For the given problem:

Group 1 : students who attend the college admissions class

Group 2 : students who do not attend the college admissions class

Students in Group 1 are different from the students in group 2. Hence A hypothesis test for the difference between two means of independent samples is appropriate

null and alternative hypotheses for this hypothesis

:   population mean exam score for students who attended the class

: population mean exam score for students who did not attend the class.

Claim:

Kelsey is looking for evidence that the population mean score of students who attend the college admissions class is greater than the population mean score of students who do not attend

i.e

> i.e - >  0

Therefore,

Null hypothesis: H_o :   - = 0

Alternate hypothesis : H_a : - >  0

Null hypothesis (H₀)

The null hypothesis states that a population parameter (such as the mean, the standard deviation, difference in means) is equal to a hypothesized value.

For the given problem, the population parameter is difference in population means; The hypothesized value is that the difference is zero i.e - = 0

Alternative Hypothesis (H₁)

The alternative hypothesis states that a population parameter is smaller, greater, or different than the hypothesized value in the null hypothesis. The alternative hypothesis is what you might believe to be true or hope to prove true.

Kelsey is looking for evidence that the population mean score of students who attend the college admissions class is greater than the population mean score of students who do not attend;

Hence the alternate hypothesis would become ;   - > 0