Math  /  Data & Statistics

QuestionAre freshmen psychology majors just as likely to change their major before they graduate compared to freshmen business majors? 428 of the 671 freshmen psychology majors from a recent study changed their major before they graduated and 426 of the 643 freshmen business majors changed their major before they graduated. What can be concluded at the α=0.05\alpha=0.05 level of significance?
For this study, we should use Select an answer a. The null and alternative hypotheses would be: H0H_{0} : Select an answer Select an answer Select an answer H1H_{1} : Select an answer Select an answer Select an answer b. The test statistic ? == \square (please show your answer to 3 decimal places.) c. The pp-value == \square (Please show your answer to 4 decimal places.) d. The pp-value is ? α\alpha e. Based on this, we should Select an answer the null hypothesis. f. Thus, the final conclusion is that ... The results are statistically significant at α=0.05\alpha=0.05, so there is sufficient evidence to conclude that the population proportion of freshmen psychology majors who change their major is different from the population proportion of freshmen business majors who change their major. The results are statistically significant at α=0.05\alpha=0.05, so there is sufficient evidence to conclude that the proportion of the 671 freshmen psychology majors who changed their major is different from the proportion of the 643 freshmen business majors who change their major. 0 The results are statistically insignificant at α=0.05\alpha=0.05, so there is insufficient evidence to conclude that the population proportion of freshmen psychology majors who change their major is different from the population proportion of freshmen business majors who change their major. The results are statistically insignificant at α=0.05\alpha=0.05, so there is statistically significant evidence to conclude that the population proportion of freshmen psychology majors who change their major is the same as the population proportion of freshmen business majors who change their major.

Studdy Solution

STEP 1

1. We are comparing two proportions: the proportion of psychology majors who change their major and the proportion of business majors who change their major.
2. The level of significance is α=0.05\alpha = 0.05.
3. We will use a two-proportion z-test to compare the proportions.

STEP 2

1. State the null and alternative hypotheses.
2. Calculate the test statistic.
3. Determine the p-value.
4. Compare the p-value with α\alpha and make a decision.
5. State the conclusion.

STEP 3

State the null and alternative hypotheses:
- H0H_0: The proportion of psychology majors who change their major is equal to the proportion of business majors who change their major. - H1H_1: The proportion of psychology majors who change their major is not equal to the proportion of business majors who change their major.

STEP 4

Calculate the test statistic using the formula for the two-proportion z-test:
p^1=428671,p^2=426643\hat{p}_1 = \frac{428}{671}, \quad \hat{p}_2 = \frac{426}{643}
p^=428+426671+643\hat{p} = \frac{428 + 426}{671 + 643}
z=p^1p^2p^(1p^)(1671+1643)z = \frac{\hat{p}_1 - \hat{p}_2}{\sqrt{\hat{p}(1-\hat{p})\left(\frac{1}{671} + \frac{1}{643}\right)}}
Calculate p^1\hat{p}_1, p^2\hat{p}_2, p^\hat{p}, and zz.

STEP 5

Calculate p^1\hat{p}_1, p^2\hat{p}_2, and p^\hat{p}:
p^1=4286710.6379\hat{p}_1 = \frac{428}{671} \approx 0.6379
p^2=4266430.6629\hat{p}_2 = \frac{426}{643} \approx 0.6629
p^=428+426671+6430.6501\hat{p} = \frac{428 + 426}{671 + 643} \approx 0.6501
Calculate zz:
z=0.63790.66290.6501×(10.6501)×(1671+1643)1.058z = \frac{0.6379 - 0.6629}{\sqrt{0.6501 \times (1-0.6501) \times \left(\frac{1}{671} + \frac{1}{643}\right)}} \approx -1.058

STEP 6

Determine the p-value using the z-table or a calculator for z=1.058z = -1.058.
The p-value is approximately 0.2905.

STEP 7

Compare the p-value with α=0.05\alpha = 0.05:
Since 0.2905>0.050.2905 > 0.05, we fail to reject the null hypothesis.

STEP 8

State the conclusion:
The results are statistically insignificant at α=0.05\alpha = 0.05, so there is insufficient evidence to conclude that the population proportion of freshmen psychology majors who change their major is different from the population proportion of freshmen business majors who change their major.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord