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 three English courses with a standard deviation of 0.8. The females took an average of four English courses with a standard deviation of 1.0. Are the means statistically the same? (Assume a 5% level of significance.) Useful tools: Normal Distribution Calculator t-Distribution Calculator a. Which of the following null and alternative hypotheses match this scenario? Ο 10: Δμ 0 H: Δμ +0 Ho: Δμ 0 H: Δμ-0 Ο Η0: Δμ=0 Ha: Δμ >0 b. Which type of test should be applied? O The alternative hypothesis indicates a right-tailed test. The alternative hypothesis indicates a left-tailed test. O The alternative hypothesis indicates a two-tailed test. c. Which type of distribution should be applied? The required distribution is a Normal Distribution. The required distribution is Student's t-Distribution. O The required distribution is a Binomial Distribution approximated by a Normal Distribution.
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 three English courses with a standard deviation of 0.8. The females took an average of four English courses with a standard deviation of 1.0. Are the means statistically the same? (Assume a 5% level of significance.) Useful tools: Normal Distribution Calculator t-Distribution Calculator a. Which of the following null and alternative hypotheses match this scenario? Ο 10: Δμ 0 H: Δμ +0 Ho: Δμ 0 H: Δμ-0 Ο Η0: Δμ=0 Ha: Δμ >0 b. Which type of test should be applied? O The alternative hypothesis indicates a right-tailed test. The alternative hypothesis indicates a left-tailed test. O The alternative hypothesis indicates a two-tailed test. c. Which type of distribution should be applied? The required distribution is a Normal Distribution. The required distribution is Student's t-Distribution. O The required distribution is a Binomial Distribution approximated by a Normal Distribution.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
- [t-Distribution Calculator](#)
#### Hypothesis Testing Steps
**a. Formulating Hypotheses**
Which null (\( H_0 \)) and alternative (\( H_a \)) hypotheses align with this scenario?
- \(\circ \, H_0: \Delta \mu = 0\)
\(\quad H_a: \Delta \mu \neq 0\)
- \(\circ \, H_0: \Delta \mu \neq 0\)
\(\quad H_a: \Delta \mu = 0\)
- \(\circ \, H_0: \Delta \mu = 0\)
\(\quad H_a: \Delta \mu > 0\)
**b. Selecting the Test Type**
Which type of test should be applied?
- \(\circ\) Right-tailed test
- \(\circ\) Left-tailed test
- \(\circ\) Two-tailed test
**c. Choosing the Appropriate Distribution**
Which distribution type is applicable?
- \(\circ\) Normal Distribution
- \(\circ\) Student's t-Distribution
- \(\circ\) Binomial Distribution approximated by a Normal Distribution
**d. Calculating the p-value**
Determine the p-value from this hypothesis test.
\[ p = \, \_\_\_\_ \]
This structured approach guides students in conducting a hypothesis test, allowing for accurate analysis of the data with the correct statistical tools and calculations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fedd99afd-48e9-4e8a-b434-1d3cd4c035a5%2F59558764-2e86-4360-8c85-343b24f49fde%2Fppfhvtd_processed.png&w=3840&q=75)
Transcribed Image Text:### Analysis of Course Enrollment by Gender
#### Scenario Description
The average number of English courses taken by male and female college students over a two-year period is believed to be equivalent. An experiment was conducted collecting data from 29 male and 16 female students. Males averaged three English courses with a standard deviation of 0.8, while females averaged four courses with a standard deviation of 1.0. We are tasked with determining if these means are statistically equivalent at a 5% significance level.
#### Useful Tools
- [Normal Distribution Calculator](#)
- [t-Distribution Calculator](#)
#### Hypothesis Testing Steps
**a. Formulating Hypotheses**
Which null (\( H_0 \)) and alternative (\( H_a \)) hypotheses align with this scenario?
- \(\circ \, H_0: \Delta \mu = 0\)
\(\quad H_a: \Delta \mu \neq 0\)
- \(\circ \, H_0: \Delta \mu \neq 0\)
\(\quad H_a: \Delta \mu = 0\)
- \(\circ \, H_0: \Delta \mu = 0\)
\(\quad H_a: \Delta \mu > 0\)
**b. Selecting the Test Type**
Which type of test should be applied?
- \(\circ\) Right-tailed test
- \(\circ\) Left-tailed test
- \(\circ\) Two-tailed test
**c. Choosing the Appropriate Distribution**
Which distribution type is applicable?
- \(\circ\) Normal Distribution
- \(\circ\) Student's t-Distribution
- \(\circ\) Binomial Distribution approximated by a Normal Distribution
**d. Calculating the p-value**
Determine the p-value from this hypothesis test.
\[ p = \, \_\_\_\_ \]
This structured approach guides students in conducting a hypothesis test, allowing for accurate analysis of the data with the correct statistical tools and calculations.
Transcribed Image Text:**Question e**: Which of the following is an appropriate conclusion?
- Given that \( p < \alpha \) at a 5% level of significance, from the sample data, there is sufficient evidence to conclude that the means are statistically the same.
- Given that \( p > \alpha \) at a 5% level of significance, from the sample data, there is sufficient evidence to conclude that the means are statistically the same.
- Given that \( p > \alpha \) at a 5% level of significance, from the sample data, there is not sufficient evidence to conclude that the means are statistically the same.
- Given that \( p < \alpha \) at a 5% level of significance, from the sample data, there is sufficient evidence to conclude that the difference in means is statistically significant.
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