![anggar20](/avatars/22606.jpg)
anggar20
30.12.2020 •
Mathematics
A consumer group is testing camp stoves. To test the heating capacity of a stove, they measure the time required to bring 2 quarts of water from 50 degrees to boiling.
Two competing models are under consideration. Thirty-six stoves of each model were tested and the following results were obtained.
Model 1: mean time is 11.4 and standard deviation is2.5
Model 2: mean time is 9.9 and standard deviation is 3.0
Is there any difference between the performances of these two models? {use a .05 level of significance}. Find the p-value of the sample statistic and do a significance test.
Find a 95% confidence interval for the difference of the means.
Solved
Show answers
More tips
- A Animals and plants How to Store Carrots: Tips for Homeowners...
- L Legal consultation Juvenile Justice: Who Needs It?...
- F Family and Home How to Choose the Best Diapers for Your Baby?...
- F Family and Home Parquet or laminate, which is better?...
- L Leisure and Entertainment How to Properly Wind Fishing Line onto a Reel?...
- L Leisure and Entertainment How to Make a Paper Boat in Simple Steps...
- T Travel and tourism Maldives Adventures: What is the Best Season to Visit the Luxurious Beaches?...
- H Health and Medicine Kinesiology: What is it and How Does it Work?...
- O Other How to Choose the Best Answer to Your Question on The Grand Question ?...
- L Leisure and Entertainment History of International Women s Day: When Did the Celebration of March 8th Begin?...
Answers on questions: Mathematics
- M Mathematics If A is in the fourth quadrant and cos A = 5/13 , find the value of (13 sin A +5secA)/(3tanA+6 cosecA)...
- M Mathematics Seven of 200 digital video recorders DVR in an inventory are known to be defective...
- M Mathematics Please give the best explanation that you can Thank you!...
- M Mathematics 8-2x=5-4x 4+3x=2-2x 2(x-1)+2(3x-1)=0...
- M Mathematics Can somebody help me Please....
- M Mathematics THE FIGURE BELOW REPRESENTS A RIGHT PYRAMID. ON A SQUARE BASE 3cm,THE SLANT EDGE IS 4cm b)CALCULATE THE SURFACE AREA OF THE PYRAMID...
- M Mathematics Help me Will mark brainliest...
- M Mathematics If the equation of the line y=-5x+7 is changed to y=5x+7, how does the graph change?...
- M Mathematics Math pls patulong You are a bank financier. Your bank pays an annual interest rate of 3% compounded quarterly. If the initial deposit (or principal), of your client is Php 50...
- M Mathematics The sum of two numbers is 40. The larger number is 8 more than the smaller number. What are the numbers?...
Ответ:
a
The decision rule is
Reject the null hypothesis
The conclusion is
There is sufficient evidence to show that there is a difference between the performances of these two models
b
The 95% confidence interval is![0.224 < \mu_1 - \mu_2 < 2.776](/tpl/images/1009/6067/3b4f8.png)
Step-by-step explanation:
From the question we are told that
The sample size is n = 36
The first sample mean is![\= x_1 = 11.4](/tpl/images/1009/6067/48399.png)
The first standard deviation is![s_1 = 2.5](/tpl/images/1009/6067/398f7.png)
The second sample mean is![\= x_2 = 9.9](/tpl/images/1009/6067/fa6dc.png)
The second standard deviation is![s_2 = 3.0](/tpl/images/1009/6067/f4005.png)
The level of significance is![\alpha = 0.05](/tpl/images/1009/6067/224ae.png)
The null hypothesis is![H_o : \mu_1 - \mu_2 = 0](/tpl/images/1009/6067/8483a.png)
The alternative hypothesis is![H_a : \mu_1 - \mu_2 \ne 0](/tpl/images/1009/6067/38710.png)
Generally the test statistics is mathematically represented as
=>![z = \frac{ ( 11.4 - 9.9) - 0 }{ \sqrt{ \frac{2.5^2 }{36} + \frac{ 3^2 }{36 } } }](/tpl/images/1009/6067/f4d3d.png)
=>![z = 2.3](/tpl/images/1009/6067/a1a4d.png)
From the z table the area under the normal curve to the left corresponding to 2.3 is
Generally the p-value is mathematically represented as
=>![p-value = 2 * 0.010724](/tpl/images/1009/6067/aa52b.png)
=>![p-value = 0.02](/tpl/images/1009/6067/ecfc5.png)
From the value obtained we see that
hence
The decision rule is
Reject the null hypothesis
The conclusion is
There is sufficient evidence to show that there is a difference between the performances of these two models
Considering question b
From the question we are told the confidence level is 95% , hence the level of significance is
=>![\alpha = 0.05](/tpl/images/1009/6067/246a1.png)
Generally from the normal distribution table the critical value of
is
Generally the margin of error is mathematically represented as
=>![E = 1.96 * \sqrt{ \frac{2.5^2 }{ 36 } + \frac{ 3^2}{36}}](/tpl/images/1009/6067/fbda8.png)
=>![E = 1.276](/tpl/images/1009/6067/75ffc.png)
Generally 95% confidence interval is mathematically represented as
=>![( 11.4 - 9.9 ) -1.276 < \mu_1 - \mu_2 < ( 11.4 - 9.9 ) + 1.276](/tpl/images/1009/6067/1cceb.png)
=>![0.224 < \mu_1 - \mu_2 < 2.776](/tpl/images/1009/6067/3b4f8.png)
Ответ:
2.