Part 4 of 7 Part 4: Using the normal approximation for the binomial distribution (without the half unit correction), what is the test statistic for this sample based on the sample proportion? 2 = 0.44 (Report answer as a decimal accurate to 2 decimal places.)
Part 4 of 7 Part 4: Using the normal approximation for the binomial distribution (without the half unit correction), what is the test statistic for this sample based on the sample proportion? 2 = 0.44 (Report answer as a decimal accurate to 2 decimal places.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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answer part4
![**Introduction:**
In a certain school district, it was observed that 24% of the students in elementary schools were classified as only children (no siblings). However, in a special program for talented and gifted children, 78 out of 249 students are only children. The school district administrators want to know if the proportion of only children in the special program is significantly different from the proportion for the school district. This is tested at the \(\alpha = 0.04\) level of significance.
**Part 1:**
- **Hypothesized Population Proportion:**
\[ p = 0.24 \]
(Report answer as a decimal accurate to 2 decimal places. Do not report using the percent symbol.)
- **Type of Hypothesis Test:**
Based on the statement of the problem, the hypothesis test has:
- Two-tailed test (selected).
**Part 2:**
- **Hypotheses:**
Choose the correct pair of hypotheses for this situation:
- \((B)\) \( H_0 : p = 0.24 \)
- \( H_1 : p \neq 0.24 \)
(Selected option).
**Part 3:**
- **Sample Proportion Value:**
\[ \hat{p} = 0.31 \]
(Report answer as a decimal accurate to 2 decimal places.)
**Part 4:**
- **Test Statistic:**
Using the normal approximation for the binomial distribution (without the half unit correction), calculate the test statistic for this sample based on the sample proportion:
\[ z = 1.80 \]
(Correct calculation indicated, initial guess was \( z = 0.44 \)).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9968cb77-9bdb-4512-9b62-942115f51f1d%2Fa418556d-a7ae-43f0-abf7-bcff83e72904%2Fjwb31t_processed.png&w=3840&q=75)
Transcribed Image Text:**Introduction:**
In a certain school district, it was observed that 24% of the students in elementary schools were classified as only children (no siblings). However, in a special program for talented and gifted children, 78 out of 249 students are only children. The school district administrators want to know if the proportion of only children in the special program is significantly different from the proportion for the school district. This is tested at the \(\alpha = 0.04\) level of significance.
**Part 1:**
- **Hypothesized Population Proportion:**
\[ p = 0.24 \]
(Report answer as a decimal accurate to 2 decimal places. Do not report using the percent symbol.)
- **Type of Hypothesis Test:**
Based on the statement of the problem, the hypothesis test has:
- Two-tailed test (selected).
**Part 2:**
- **Hypotheses:**
Choose the correct pair of hypotheses for this situation:
- \((B)\) \( H_0 : p = 0.24 \)
- \( H_1 : p \neq 0.24 \)
(Selected option).
**Part 3:**
- **Sample Proportion Value:**
\[ \hat{p} = 0.31 \]
(Report answer as a decimal accurate to 2 decimal places.)
**Part 4:**
- **Test Statistic:**
Using the normal approximation for the binomial distribution (without the half unit correction), calculate the test statistic for this sample based on the sample proportion:
\[ z = 1.80 \]
(Correct calculation indicated, initial guess was \( z = 0.44 \)).
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