Answered: The mean number of English courses…

Name: The mean number of English courses taken in a two-year time period by
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: The mean number of English courses taken in a two-year time period by male and female college students is believed to be about the same. An experiment is conducted and data are collected from 29 males and 16 females. The males took an average of two

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Topic Video

Question

The mean number of English courses taken in a two-year time period by male and female college students is believed to be about the same. An experiment is conducted and data are collected from 29 males and 16 females. The males took an average of two English courses with a standard deviation of 0.7. The females took an average of three English courses with a standard deviation of 1.1. Are the means statistically the same? (Use

? = 0.05)

NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

The following text appears on an educational website related to a statistical hypothesis test regarding English course enrollment among college students:

**Problem Statement:**
The mean number of English courses taken over a two-year period by male and female college students is believed to be approximately the same. An experiment is conducted using data from 29 males and 16 females. The males took an average of two English courses with a standard deviation of 0.7. The females took an average of three English courses with a standard deviation of 1.1. The question posed is whether the means are statistically the same with a significance level of $ \alpha = 0.05 $.

**Instructions and Solutions:**

- **Part (d):**
**Question:** State the distribution to use for the test. (Your answer should be in the form $ z $ or $ t_{df} $ where $ df $ is the degrees of freedom. Round to two decimal places.)
**Given Answer:** $ t_{44} $
**Correction:** The answer chosen was marked incorrect.

- **Part (f):**
**Question:** What is the p-value? (Round your answer to four decimal places.)
**Given Answer:** 0.0249
**Correction:** The answer chosen was marked incorrect.

**Explanation of p-value choice:**
- “If $ H_0 $ is false, then there is a chance equal to the p-value that the difference in the sample mean number of English courses taken by males and females is at least 1.”
- This choice was marked correct.

This setup engages students in the process of applying hypothesis testing, interpreting statistical results, and understanding the implications of p-values in testing the null hypothesis.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Hypothesis Tests and Confidence Intervals for Means$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions