Homework Help is Here – Start Your Trial Now!
Math
Statistics
7. Questions 4, 5, and 6 all have 90% confidence level. Why are the crit values different for all three?

7. Questions 4, 5, and 6 all have 90% confidence level. Why are the crit values different for all three?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question

Only Question 7 i need the answer 

 
 
 
### Problem 4 It has been accepted that 40% or less of households changed their driving habits because of escalating gas prices. However, a popular energy company challenges that more than 40% of households have changed their driving habits because of escalating gas prices. Their recent survey of 180 households finds that 70 households have made lifestyle changes due to escalating gas prices. At a 10% level of significance, test the energy company's challenge. #### Hypotheses - \( H_0: p \leq 0.40 \) - \( H_a: p > 0.40 \) #### Calculations - \( x = 70 \) - \( n = 180 \) - \( \hat{p} = \frac{70}{180} = 0.3889 \) - \( z = \frac{0.3889 - 0.40}{\sqrt{\frac{0.40 \times 0.60}{180}}} = -0.31 \) #### Normal Curve Representation The curve shows a normal distribution with the rejection region marked in the right tail. The critical z-value (\( Z_{crit} \)) is 1.28 for a significance level (\( \alpha \)) of 0.10. #### Decision \( Z_{stat} = -0.31 \). Since \( Z_{stat} < Z_{crit} \), fail to reject \( H_0 \). - p-value = 0.3783 ### Problem 5 Every year, the Hometown Hardware Store expects an average of $606.40 per local family to be spent on springtime home repairs. A new analyst in the store disputes this and challenges that the average spending per local family will differ from this amount. A test is conducted on a random sample of 30 households, using a 90% confidence level, resulting in a sample mean of $632.85. The spending is normally distributed with a population standard deviation of $65. #### Hypotheses - \( H_0: \mu = 606.40 \) - \( H_a: \mu \neq 606.40 \) #### Calculations - \( \mu = 632.85 \) - \( \sigma = 65 \) - \( n = 30 \) - Standard Error = \( \frac{65}{\sqrt{30}} \) - \( z
Transcribed Image Text:### Problem 4 It has been accepted that 40% or less of households changed their driving habits because of escalating gas prices. However, a popular energy company challenges that more than 40% of households have changed their driving habits because of escalating gas prices. Their recent survey of 180 households finds that 70 households have made lifestyle changes due to escalating gas prices. At a 10% level of significance, test the energy company's challenge. #### Hypotheses - \( H_0: p \leq 0.40 \) - \( H_a: p > 0.40 \) #### Calculations - \( x = 70 \) - \( n = 180 \) - \( \hat{p} = \frac{70}{180} = 0.3889 \) - \( z = \frac{0.3889 - 0.40}{\sqrt{\frac{0.40 \times 0.60}{180}}} = -0.31 \) #### Normal Curve Representation The curve shows a normal distribution with the rejection region marked in the right tail. The critical z-value (\( Z_{crit} \)) is 1.28 for a significance level (\( \alpha \)) of 0.10. #### Decision \( Z_{stat} = -0.31 \). Since \( Z_{stat} < Z_{crit} \), fail to reject \( H_0 \). - p-value = 0.3783 ### Problem 5 Every year, the Hometown Hardware Store expects an average of $606.40 per local family to be spent on springtime home repairs. A new analyst in the store disputes this and challenges that the average spending per local family will differ from this amount. A test is conducted on a random sample of 30 households, using a 90% confidence level, resulting in a sample mean of $632.85. The spending is normally distributed with a population standard deviation of $65. #### Hypotheses - \( H_0: \mu = 606.40 \) - \( H_a: \mu \neq 606.40 \) #### Calculations - \( \mu = 632.85 \) - \( \sigma = 65 \) - \( n = 30 \) - Standard Error = \( \frac{65}{\sqrt{30}} \) - \( z
Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
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 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…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
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
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS