MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![**A decade-old study found that the proportion, \( p_0 \), of high school seniors who believed that "getting rich" was an important personal goal was 80%. A researcher decides to test whether or not that percentage still stands. He finds that, among the 235 high school seniors in his random sample, 170 believe that "getting rich" is an important goal. Can he conclude, at the 0.01 level of significance, that the proportion has indeed changed?**
Perform a two-tailed test. Then complete the parts below.
Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)
(a) State the **null hypothesis** \( H_0 \) and the **alternative hypothesis** \( H_1 \).
\[H_0: \]
\[H_1: \]
(b) Determine the type of **test statistic** to use.
(Choose one) [Dropdown with options]
(c) Find the value of the test statistic. (Round to three or more decimal places.)
\[ \text{Test Statistic:} \]
(d) Find the **p-value**. (Round to three or more decimal places.)
\[ \text{p-value:} \]
(e) Can we conclude that the proportion of high school seniors who believe that "getting rich" is an important goal has changed?
\[ \text{Yes} \quad \Box \quad \text{No} \quad \Box \]
**Symbols Key:**
The image contains a list of symbols typically used in statistical equations, such as:
- \( \mu, \sigma, p, \bar{x}, s, \hat{p} \)
- Subscript and superscript boxes
- Less than, greater than, equal symbols, etc.](https://content.bartleby.com/qna-images/question/1d3f2bfb-a5cc-4b06-99e2-b36f9d38db79/0751a96b-13fd-4dc3-93ba-cd77f8b6f9d0/xsm6ste_processed.jpeg)
Transcribed Image Text:**A decade-old study found that the proportion, \( p_0 \), of high school seniors who believed that "getting rich" was an important personal goal was 80%. A researcher decides to test whether or not that percentage still stands. He finds that, among the 235 high school seniors in his random sample, 170 believe that "getting rich" is an important goal. Can he conclude, at the 0.01 level of significance, that the proportion has indeed changed?**
Perform a two-tailed test. Then complete the parts below.
Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)
(a) State the **null hypothesis** \( H_0 \) and the **alternative hypothesis** \( H_1 \).
\[H_0: \]
\[H_1: \]
(b) Determine the type of **test statistic** to use.
(Choose one) [Dropdown with options]
(c) Find the value of the test statistic. (Round to three or more decimal places.)
\[ \text{Test Statistic:} \]
(d) Find the **p-value**. (Round to three or more decimal places.)
\[ \text{p-value:} \]
(e) Can we conclude that the proportion of high school seniors who believe that "getting rich" is an important goal has changed?
\[ \text{Yes} \quad \Box \quad \text{No} \quad \Box \]
**Symbols Key:**
The image contains a list of symbols typically used in statistical equations, such as:
- \( \mu, \sigma, p, \bar{x}, s, \hat{p} \)
- Subscript and superscript boxes
- Less than, greater than, equal symbols, etc.
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