Answered: What does “statistically significant”…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

When dating someone, what matters more to you: looks or personality? This question was the focus of a community college student’s class project for an introductory statistics course. She devised a 25-point scale. An answer of 1 means “personality matters most and looks don’t matter at all.” A score of 25 means “looks matter most and personality does not matter at all.” Her hypothesis is that the mean scores for males and females will differ, but she does not have an opinion about which population will have a higher mean score.

Here are her hypotheses.

H₀: μ₁ − μ₂ = 0
H_a: μ₁ − μ₂ ≠ 0

She chose a random sample of 10 classes from the schedule at Los Medanos College and distributed surveys in those classes. Survey respondents totaled 170 students: 85 females and 85 males.

We used her data to run a hypothesis test for a difference in two population means. Here are the descriptive statistics:

(picture attached)

1. Verify in the print-out above, that the difference between the sample means about 2.62 points, with the mean for females lower.

2. Question: When conducting a two-samples t test, what will we do with the values seen in the table above for standard error of the mean, minimum, and maximum for both samples. Answer: Nothing! The analysis focuses on the difference between population means so we won't use standard error for the individual means. What's the lesson? Clean up your tables! Present the descriptive statistics that will help your audience understand the results and eliminate information that is not useful.

What does “statistically significant” mean in this context? (More than one answer is correct. Select each correct answer.)

Group of answer choices (more than one could be correct)

a) Statistically significant means that we have confidence that we could draw two more random samples - one female and one male - from the same populations and we could conduct a test of hypothesis on the new samples and we could expect to come to the same hypothesis-testing conclusion.

b) Statistically significant also means "big" - there is a big difference in the means of the male and female populations.

c) Statistically significant means “probably not due to chance.” The p-value is the probability of getting this difference between sample means if the null hypothesis is true and there is no difference between the means of the two populations. In this context, if there is no gender difference in mean rating for females and males, then it is highly unlikely that we’ll get a difference between samples means as large as that observed in the data we collected.