MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
expand_more
expand_more
format_list_bulleted
Related questions
Question
A simple random sample of front-seat occupants involved in car crashes is obtained. Among3000occupants not wearing seat belts,36were killed. Among 7697occupants wearing seat belts,18were killed. Use a0.05significance level to test the claim that seat belts are effective in reducing fatalities. Complete parts (a) through (c) below.
![### Educational Text on Hypothesis Testing and Confidence Intervals for Seat Belt Effectiveness
A simple random sample of front-seat occupants involved in car crashes is analyzed. The study includes data on 3000 occupants not wearing seat belts, where 36 were killed, and 7697 occupants wearing seat belts, where 18 were killed. A significance level of 0.05 is used to test the hypothesis that seat belts are effective in reducing fatalities.
#### a. Hypothesis Test
**Null and Alternative Hypotheses:**
- **H0 (Null Hypothesis):** \( p_1 = p_2 \)
- **H1 (Alternative Hypothesis):** \( p_1 \neq p_2 \)
Where \( p_1 \) represents the fatality rate of occupants not wearing seat belts, and \( p_2 \) represents the fatality rate of occupants wearing seat belts.
**Steps:**
1. **Identify the Test Statistic (z-value):**
Enter the calculated z-value: [_____].
*(Round to two decimal places as needed.)*
2. **Identify the P-value:**
Enter the calculated P-value: [_____].
*(Round to three decimal places as needed.)*
3. **Conclusion Based on Hypothesis Test:**
Evaluate the P-value with respect to the significance level, \(\alpha = 0.05\).
- If the P-value is (1) [less than/greater than] the significance level, (2) [fail to reject/reject] the null hypothesis.
- Based on this, determine if there is (3) [sufficient/insufficient] evidence to support the claim that the fatality rate is higher for those not wearing seat belts.
#### b. Constructing a Confidence Interval
**The Appropriate Confidence Interval:**
- Calculate and provide the interval for \( p_1 - p_2 \): [_____], [_____].
*(Round to three decimal places as needed.)*
**Conclusion Based on Confidence Interval:**
- Analyze if the confidence interval limits (4) [include/do not include] 0.
- If values are both (6) [positive and negative/only positive/only negative], evaluate if the fatality rate is (7) [higher/lower/the same] for those not wearing seat belts as compared to those wearing them.
#### c. Effectiveness of Seat Belts](https://content.bartleby.com/qna-images/question/717e652d-d2e5-48fc-b5bd-80fe3da265db/eb25251d-9795-45f8-9827-de775c4a4bae/60obkw_processed.png)
Transcribed Image Text:### Educational Text on Hypothesis Testing and Confidence Intervals for Seat Belt Effectiveness
A simple random sample of front-seat occupants involved in car crashes is analyzed. The study includes data on 3000 occupants not wearing seat belts, where 36 were killed, and 7697 occupants wearing seat belts, where 18 were killed. A significance level of 0.05 is used to test the hypothesis that seat belts are effective in reducing fatalities.
#### a. Hypothesis Test
**Null and Alternative Hypotheses:**
- **H0 (Null Hypothesis):** \( p_1 = p_2 \)
- **H1 (Alternative Hypothesis):** \( p_1 \neq p_2 \)
Where \( p_1 \) represents the fatality rate of occupants not wearing seat belts, and \( p_2 \) represents the fatality rate of occupants wearing seat belts.
**Steps:**
1. **Identify the Test Statistic (z-value):**
Enter the calculated z-value: [_____].
*(Round to two decimal places as needed.)*
2. **Identify the P-value:**
Enter the calculated P-value: [_____].
*(Round to three decimal places as needed.)*
3. **Conclusion Based on Hypothesis Test:**
Evaluate the P-value with respect to the significance level, \(\alpha = 0.05\).
- If the P-value is (1) [less than/greater than] the significance level, (2) [fail to reject/reject] the null hypothesis.
- Based on this, determine if there is (3) [sufficient/insufficient] evidence to support the claim that the fatality rate is higher for those not wearing seat belts.
#### b. Constructing a Confidence Interval
**The Appropriate Confidence Interval:**
- Calculate and provide the interval for \( p_1 - p_2 \): [_____], [_____].
*(Round to three decimal places as needed.)*
**Conclusion Based on Confidence Interval:**
- Analyze if the confidence interval limits (4) [include/do not include] 0.
- If values are both (6) [positive and negative/only positive/only negative], evaluate if the fatality rate is (7) [higher/lower/the same] for those not wearing seat belts as compared to those wearing them.
#### c. Effectiveness of Seat Belts
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution
Trending nowThis is a popular solution!
Step by stepSolved in 4 steps
Knowledge Booster
Similar questions
- 90%arrow_forwardThe length of fish were measured at 3 different lakes. Lake 1: 3.5, 4.2, 6.1, 5.2 Lake 2: 5.1, 6.2, 5.3, 2.1 Lake 3: 5.6, 7.1, 2.4, 4.1, 6.2 Enter the test statistic (to 4 decimal places)arrow_forwardresearchers wanted to determine if carpeted rooms contained more baterica than uncapted rooms. to determine the amount of bacterica in a room reseachers pumpled the air from the room over a petri dish at the rate of 1 cubic foot per minute for eight carpeted rooms and eight uncaprted rooms. colonies of baterica were alled to form in 16 petri dishes. the results shown below are the baterica counta per cubic foot mean standard deviation sample size capeted room 11.2 2.6774 8 uncapted room 9.7875 3.21 8 you want ti test using sigificance level of 0.01 whether the mean bactiria count is high for carpeted rooms than for uncapteed rooms. test whether the mean bacteria count is high for carpeted rooms thatn uncarpeted rooms. show all steps using the p value method. what is Ho and H1? what is the test statsic and p value? what conclusion can be made?arrow_forward
- Please help me in answering the following practice question:Given a random sample of the amount of protein (in gram) in one bag of snack food: 0.95, 0.85, 0.92, 0.95, 0.93, 0.86, 1, 0.92, 0.85, 0.81, 0.78, 0.93, 0.93, 1.05, 0.93, 1.06, 1.06, 0.96, 0.81, 0.96 Here, it is assumed that the amount of protein in the snack is normal. How would I calculate a 98% two-sided confidence interval for the average amount of protein in one bag?Thank you for your help in advance!arrow_forwardYou want to compare differences in prior arrests across ethnicity in your study, you measured ethnicity as white =0 black =1 hispanic=2, and other =3. Prior arrests was recorded as the number of prior arrests. which test would you perform to see if arrests differ across diffrent ethnic categories? A. ANOVA B. T-testarrow_forwardCan someone please answer d.) e.) and f.)arrow_forward
- You decide that you want to make sure your estimate from part a is correct. You go out and gather 10 simple random samples of 25 people in your school and calculate the proportion of students within each sample whose Amazon packages arrive within two business days of ordering. The proportion of customers that receive their packages within two days of ordering are given below. 0.70, 0.75, 0.6, 0.95, 0.90, 0.73, 0.87, 0.86, 0.92, 0.97 Explain why all of the sample proportions are not the same.arrow_forwardA researcher collected how many grams of fat people on a specific diet consumed at breakfast and at lunch. The data for a sample of 8 people is shown in the table below. xx 11.3 8.2 7.2 3.6 2.3 2.5 2.7 0.4 yy 13.7 10.7 10.2 7.2 6.3 6.5 6.1 4.1 xx = grams of fat in breakfastyy = grams of fat in lunchThis data can be modeled by the equation ˆy=0.84x+4.07.y^=0.84x+4.07.Given this, how many grams of fat in lunch would be expected for a person who consumed 1.2 grams of fat at breakfast? Round to 1 decimal place.Answer =arrow_forwardRandom samples of students at 107 four-year colleges were interviewed several times since 1998. Of the students who reported drinking alcohol, the percentage who reported bingeing at least three times within the past two weeks was 41.1% of 336 students in 1998 and 21.6% of 843 students in 2004. a. Estimate the difference between the proportions in 2004 and 1998, and interpret. b. Find the standard error for this difference. Interpret it. c. Define the two relevant population parameters to compare in the context of this exercise. d. Construct and interpret a 90% confidence interval to estimate the true difference. e. State the assumptions for the confidence interval in part d to be valid. ... A. The number of students in the population in 2004 who reported drinking alcohol that binged at least three times within the past two weeks. B. The proportion of the student population in 1998 who reported drinking alcohol that binged at least three times within the past two weeks. C. The number…arrow_forward
- In a simple random sample of 1200 young people, 86% had earned a high school diploma. What is the standard error for this estimate of the percentage of all young people who earned a high school diploma?arrow_forwardThe average spent nationally on Christmas gifts in 2020 was reported to be $650 per person. Below is a random sample of gift givers from Iowa and what they spent in 2020. Is there sufficient evidence to conclude that Iowans spend less than the national average? Estimate the average amount spent by Iowans on Christmas gifts in 2020 with a 90%-CI. 700 450 400 525 550 550 600 575 650 625 500arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning 
Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSON
The Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. Freeman
Introduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman