Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. statistics
  3. a car company is considering a new engine filt

A car company is considering a new engine filter for its new hybrid automobile line. But...

Free

50.1K

Verified Solution

Question

Statistics

A car company is considering a new engine filter for its newhybrid automobile line. But it does not want to switch to the newbrand unless there is evidence that the new filter can improve fueleconomy for the vehicle (miles per gallon). The experimental designis set up so that each of the 10 cars drive the same course twice -once with the old filtration system and once with the new version.The data collected is shown below:

Car #Current FilterNew Filter
17.67.3
25.17.2
310.46.8
46.910.6
55.68.8
67.98.7
75.45.7
85.78.7
95.58.9
105.37.1

Conduct a hypothesis testing to determine whether the newfiltration system is superior. Provide the p-value from youranalysis.

Answer & Explanation Solved by verified expert
4.2 Ratings (677 Votes)

Current Filter New Filter Difference
7.6 7.3 0.3
5.1 7.2 -2.1
10.4 6.8 3.6
6.9 10.6 -3.7
5.6 8.8 -3.2
7.9 8.7 -0.8
5.4 5.7 -0.3
5.7 8.7 -3
5.5 8.9 -3.4
5.3 7.1 -1.8

Sample mean of the difference using excel function AVERAGE(), xÌ…d = -1.4400

Sample standard deviation of the difference using excel function STDEV.S() sd = 2.2406

Sample size, n = 10

Null and Alternative hypothesis:  

Ho : µd =    0

H1 : µd <    0

Test statistic:  

t = (x̅d)/(sd/√n) = (-1.44)/(2.2406/√10) =    -2.0323

df = n-1 =    9

p-value :  

Left tailed p-value = T.DIST(-2.0323, 9, 1) =    0.0363

Decision:  

p-value < 0.05, Reject the null hypothesis  

Conclusion:  

There is enough evidence to conclude that  the new filtration system is superior at 0.05 significance level.
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Biology
1.2K views

g each option to the correct location on the image tch each effect to the...

Biology
1.2K views

Stimulated B lymphocytes switch from the synthesis of membrane-bound to secreted antibody molecules by increasing the concentration...

Chemistry
1.2K views

Use the Henderson-Hasselbach equation to calculate the pH of each solution: I figured out part A by...

Physics
1.2K views

Suppose 24 kg of 90.5 C water is placed in contact with 24 kg of...

Physics
1.2K views

A toy top of constant density do is constructed from a portion of a solid...

Basic Math
1.2K views

Find the size of the matrix 3 1 3 0 A 4 1 5 5

Algebra
1.2K views

Set up a Newton iteration to compute the square root of given positive number C...

Accounting
1.2K views

Reardon Retail Company consists of two stores, A and B. Store A had sales of...

Accounting
1.2K views

For financial accounting and external reporting purposes, all selling and administrative expenses are treated as

Accounting
1.2K views

Si una empresa tiene una razn de endeudamiento (es decir, D/A) de 44%, cul es...

Accounting
1.2K views

\table[[Cash,Debit,Credit],[Accounts receivable,$19,100,],[Inventory,10,200,],[Prepaid rent,15,620,],[Equipment,480,],[Accumulated depreciation-equipment,16,705,],[Accounts payable,,1,800],[Unearned service revenue,,4,100],[Common stock,,765],[Retained earnings,,10,300],[Dividends,,33,050],[Sales revenue,9,600,],[Rent expense,,129,600],[Cost of goods sold,15,760,],[Salaries and...

Accounting
1.2K views

I need a break down on this because I can't figure how what steps I'm...