Random samples of 54 male students and 53 female students at the U of A were asked to state their car preference (American, European, and Japanese). The resulting frequencies are shown in the following table. Is there enough evidence to conclude a difference in car preference between males and females? American European Japanese -.... :Male 18 Female (a) In performing this statistical test, state the hypotheses. O Họ: the distribution of preference is not the same for males and females vs. HA: the distribution of preference is the same for males and females O Họ: the distribution of gender is not the same for each car preference vs. Ha: the distribution of gender is the same for each car preference O Họ: the distribution of preference is the same for males and females vs. Ha: the distribution of preference is not the same for males and females O Họ: the proportion of females is the same for each car preference vs. Ha: the proportion of females is not the same for each car preference O Họ: the proportion of males is the same for each car preference vs. Hạ: the proportion of males is not the same for each car preference (b) What is the expected frequencies of each cell? Fill out the table. (Round your answers to 2 decimal places, if needed.) American European Japanese - .. Male 15.14 Female 20.8 (c) What is the test statistic value for this hypothesis test? (Round your answers to 2 decimal places, if needed.) TS = (d) The test statistic follows a chi-square distribution with df = 2 (e) Using the statistical table, the p-value is 0.01 < p-value < 0.025 + () Based on the p-value, those conducting the test should fail to reject the null hypothesis at the significance level of 0.05.
Random samples of 54 male students and 53 female students at the U of A were asked to state their car preference (American, European, and Japanese). The resulting frequencies are shown in the following table. Is there enough evidence to conclude a difference in car preference between males and females? American European Japanese -.... :Male 18 Female (a) In performing this statistical test, state the hypotheses. O Họ: the distribution of preference is not the same for males and females vs. HA: the distribution of preference is the same for males and females O Họ: the distribution of gender is not the same for each car preference vs. Ha: the distribution of gender is the same for each car preference O Họ: the distribution of preference is the same for males and females vs. Ha: the distribution of preference is not the same for males and females O Họ: the proportion of females is the same for each car preference vs. Ha: the proportion of females is not the same for each car preference O Họ: the proportion of males is the same for each car preference vs. Hạ: the proportion of males is not the same for each car preference (b) What is the expected frequencies of each cell? Fill out the table. (Round your answers to 2 decimal places, if needed.) American European Japanese - .. Male 15.14 Female 20.8 (c) What is the test statistic value for this hypothesis test? (Round your answers to 2 decimal places, if needed.) TS = (d) The test statistic follows a chi-square distribution with df = 2 (e) Using the statistical table, the p-value is 0.01 < p-value < 0.025 + () Based on the p-value, those conducting the test should fail to reject the null hypothesis at the significance level of 0.05.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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![### Hypothesis Testing of Car Preferences by Gender
**Background:**
Random samples of 54 male students and 53 female students at the U of A were asked to state their car preference among American, European, and Japanese cars. The resulting frequencies are shown below. The question is whether there is enough evidence to conclude a difference in car preference between males and females.
**Frequency Table:**
| | American | European | Japanese |
|----------|----------|----------|----------|
| Male | 18 | 12 | 24 |
| Female | 12 | 23 | 18 |
**Tasks:**
**(a) Hypotheses:**
- **\(H_0\):** The distribution of preference is not the same for males and females.
- **\(H_A\):** The distribution of preference is the same for males and females.
**(b) Expected Frequencies:**
Calculate the expected frequencies for each cell. The values are rounded to two decimal places.
| | American | European | Japanese |
|----------|----------|----------|----------|
| Male | 15.14 | 19.86 | 19.00 |
| Female | 14.86 | 15.14 | 15.00 |
**(c) Test Statistic Value:**
\[ TS = \]
**(d) Test Statistic Distribution:**
The test statistic follows a chi-square distribution with degrees of freedom (df) = 2.
**(e) P-value:**
Using the statistical table, the p-value is:
\[ 0.01 < p\text{-value} < 0.025 \]
**(f) Conclusion Based on P-value:**
Based on the p-value, those conducting the test should **fail to reject** the null hypothesis at the significance level of 0.05.
**(g) Appropriate Conclusion:**
- There is insufficient evidence to conclude there is a difference in males and females for car preference.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F650192d1-d2bd-4507-bb57-c42486ecf22d%2Fd21e4453-1636-4592-bfc0-0023e59b6a45%2Fcv037p8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing of Car Preferences by Gender
**Background:**
Random samples of 54 male students and 53 female students at the U of A were asked to state their car preference among American, European, and Japanese cars. The resulting frequencies are shown below. The question is whether there is enough evidence to conclude a difference in car preference between males and females.
**Frequency Table:**
| | American | European | Japanese |
|----------|----------|----------|----------|
| Male | 18 | 12 | 24 |
| Female | 12 | 23 | 18 |
**Tasks:**
**(a) Hypotheses:**
- **\(H_0\):** The distribution of preference is not the same for males and females.
- **\(H_A\):** The distribution of preference is the same for males and females.
**(b) Expected Frequencies:**
Calculate the expected frequencies for each cell. The values are rounded to two decimal places.
| | American | European | Japanese |
|----------|----------|----------|----------|
| Male | 15.14 | 19.86 | 19.00 |
| Female | 14.86 | 15.14 | 15.00 |
**(c) Test Statistic Value:**
\[ TS = \]
**(d) Test Statistic Distribution:**
The test statistic follows a chi-square distribution with degrees of freedom (df) = 2.
**(e) P-value:**
Using the statistical table, the p-value is:
\[ 0.01 < p\text{-value} < 0.025 \]
**(f) Conclusion Based on P-value:**
Based on the p-value, those conducting the test should **fail to reject** the null hypothesis at the significance level of 0.05.
**(g) Appropriate Conclusion:**
- There is insufficient evidence to conclude there is a difference in males and females for car preference.
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