Hypothesis Tests - 2 samples x C Solved: One of the questions b Answered: The mean numbero x P Holiday Hits Radio - Now i webassign.net/web/Student/Assignment-Responses/submit?dep=24266165&tags=autosave#question3964178_7 O Part (c) O Part (d) State the distribution to use for the test. (Enter your answer in the form z or tor where df is the degrees of freedom. Round your answer to two decimal places.) 12.02 O Part (e) O Part () What is the p-value? (Round your answer to four decimal places.) 0.0005 Explain what the p-value means for this problem. O If Ho is true, 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 most 1. O If Ho is true, 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. O If Ho 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 most 1. O If Ho 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. O Part (g) O Part (h) O Part (1) Explain how you determined which distribution to use. O The t-distribution will be used because the samples are dependent. O The standard normal distribution will be used because the samples involve the difference in proportions. O The standard normal distribution will be used because the samples are independent and the population standard deviation is known. O The t-distribution will be used because the samples are independent and the population standard deviation is not known.

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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

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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.)

**Hypothesis Tests - 2 Samples**

**Part (e)**
- **Task:** State the distribution to use for the test. (Enter your answer in the form $ z $ or $ t_{df} $ where $ df $ is the degrees of freedom. Round your answer to two decimal places.)
- **Response:** $ t_{2.02} $ (Incorrect indication shown by a cross).

**Part (f)**

- **Question:** What is the p-value? (Round your answer to four decimal places.)
- **Response:** 0.0005 (Incorrect indication shown by a cross).

- **Explanation of the p-value:**
- Options provided:
1. If $ H_0 $ is true, 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 most 1.
2. **(Selected Option)** If $ H_0 $ is true, 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.
3. 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 most 1.
4. 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.
- The selected option is correct as indicated by a check mark.

**Part (i)**

- **Explanation of distribution choice:**
- Options provided:
1. The t-distribution will be used because the samples are dependent.
2. The standard normal distribution will be used because the samples involve the difference in proportions.
3. **(Selected Option, Incorrect)** The standard normal distribution will be used because the samples are independent and the population standard deviation is known.
4. The t-distribution will be used because the samples are independent and the population standard deviation is not known.

- The selected option is incorrect as indicated by a cross mark.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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