Question

Students enrolled in an introductory statistics course at a university were asked to take a survey that indicated whether the student’s learning style was more visual or verbal. Each student received a numerical score ranging from -11 to +11. Negative scores indicated a visual learner, and positive scores indicated a verbal learner. The closer the score was to -11 or +11, the stronger the student’s inclination toward that learning style. A score of 0 would indicate neutrality between visual or verbal learning. For the 36 students who took the survey, the mean score was -2.744, and the standard deviation was 4.988.

1. State the null and alternative hypotheses for testing whether the mean score (among all students at this university) differs from 0.

2. Calculate the value of the t-test statistic for the hypotheses stated in question 1.

3. Determine the p-value of the test as accurately as possible.

4. Summarize the conclusion that you would draw from this test.

5. Comment on whether the technical conditions of this t-test are satisfied.

Answer 1

Here, we have to use one sample t test for the population mean.

Part 1

The null and alternative hypotheses are given as below:

Null hypothesis: H₀: the mean score (among all students at this university) is not differs from 0.

Alternative hypothesis: H_a: the mean score (among all students at this university) differs from 0.

H₀: µ = 0 versus H_a: µ ≠ 0

This is a two tailed test.

Part 2

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

µ = 0

Xbar = -2.744

S = 4.988

n = 36

df = n – 1 = 35

α = 0.05

Critical value = - 2.0301 and 2.0301

(by using t-table or excel)

t = (Xbar - µ)/[S/sqrt(n)]

t = (-2.744 - 0)/[ 4.988/sqrt(36)]

t = -3.3007

Part 3

P-value = 0.0022

(by using t-table)

Part 4

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that the mean score (among all students at this university) differs from 0.

Part 5

The technical conditions are satisfied as the sample size can be consider small and the value of the population standard deviation is not given, so we can use t-test for the population mean.