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.

Answer:

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  [tex] 0.224   <  \mu_1 - \mu_2  < 2.776  [/tex]

Step-by-step explanation:

From the question we are told that

    The sample size is  n  =  36

    The first sample mean is  [tex]\= x_1 = 11.4[/tex]

    The first standard deviation is  [tex]s_1 = 2.5[/tex]

    The second sample mean is   [tex]\= x_2 = 9.9[/tex]

     The second standard deviation is  [tex]s_2 = 3.0[/tex]

      The level of significance is  [tex]\alpha = 0.05[/tex]

The null hypothesis is  [tex]H_o : \mu_1 - \mu_2 = 0[/tex]

The alternative hypothesis is [tex]H_a : \mu_1 - \mu_2 \ne 0[/tex]

Generally the test statistics is mathematically represented as

      [tex]z = \frac{ (\= x_1 - \= x_2 ) - (\mu_1 - \mu_2 ) }{ \sqrt{ \frac{s_1^2 }{n} + \frac{s_2^2 }{ n} } }[/tex]

=>    [tex]z = \frac{ ( 11.4 - 9.9) - 0 }{ \sqrt{ \frac{2.5^2 }{36} + \frac{ 3^2 }{36 } } }[/tex]

=>     [tex]z = 2.3[/tex]

From the z table  the area under the normal curve to the left corresponding to  2.3 is  

       [tex]P( Z > 2.3 ) = 0.010724[/tex]

Generally the p-value is mathematically represented as

      [tex]p-value = 2 * P( Z > 2.3 )[/tex]

=>    [tex]p-value = 2 * 0.010724[/tex]

=>    [tex]p-value = 0.02[/tex]

From the value obtained we see that  [tex]p-value < \alpha[/tex] 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    

      [tex]\alpha = (100 - 95 ) \%[/tex]

=>   [tex]\alpha = 0.05[/tex]

Generally from the normal distribution table the critical value  of  [tex]\frac{\alpha }{2}[/tex] is  

   [tex]Z_{\frac{\alpha }{2} } =  1.96[/tex]

Generally the margin of error is mathematically represented as  

      [tex]E = Z_{\frac{\alpha }{2} } *  \sqrt{ \frac{s_1^2 }{n } + \frac{s_2^2}{n}} [/tex]

 => [tex]E = 1.96  *    \sqrt{ \frac{2.5^2 }{ 36 } + \frac{ 3^2}{36}}  [/tex]

  => [tex]E = 1.276   [/tex]

Generally 95% confidence interval is mathematically represented as  

      [tex]( \= x_1 - \= x_2) -E <  \mu_1 - \mu_2  < ( \= x_1 - \= x_2) + E [/tex]

=>  [tex]( 11.4 - 9.9 ) -1.276  <  \mu_1 - \mu_2 < ( 11.4 - 9.9 ) + 1.276   [/tex]

=>  [tex] 0.224   <  \mu_1 - \mu_2  < 2.776  [/tex]

Please help me....... ​

Find the amount of state tax withheld if your Gross pay is $43,300, and the tax rate 5%

A. $2156
B. $2165
C. $1965
D. $1959

2 markers fewer than m packs of markers that have 9 markers in each pack

For a car that gets 21 miles per gallon, how far can it travel on 2/3 gallons?

which number is rational
A. square root of 16/6
B square root of 6
C. square root of 36/16
D. square root of 36/6

Write a story problem using the measurement interpretation of division for the following ¾ ÷ ⅛

Plz help me with this plz I am marking branliest to correct answer plzzzzz

Amelia wants to rearrange the furniture in her room. She makes a scale drawing of her rectangular room,
in which every 2 inches represents 5 feet. On her scale drawing, the area of the room is 24.96 square
inches. If one side of her room is 12 feet long, how long is the other side of her room, in feet?

question: select the appropriate linear equation for the trend line
I NEED HELP! <3
A. y = x + 1
B. y = -x -1
C. y = x -1
D. y = -x + 1

Translate this sentence into an equation. The sum of 18 and Mabel's savings is 49. Use the variable m to represent Mabel's saving

A machine fills boxes at a constant rate. At the end of 35 minutes, it has filled 5 boxes. Which table represents the relationship between the number of minutes the machine fills boxes and the number of boxes it has filled?

Which system of equations has no solution?

5 x + 5 y = 10 and 2 x + 2 y = 4

3 x minus 6 y = 4 and negative 4 x + 8 y = 7

6 x + 2 y = 6 and 7 x + 3 y = 9

3 x minus 4 y = 16 and 2 x + 3 y = 5

Question #2

Two linear equations are represented by using the tables below.

A 2-column table with 4 rows is titled Equation A. Column 1 is labeled x with entries negative 5, negative 2, 0, 1. Column 2 is labeled y with entries negative 4, negative 1, 1, 2.
A 2-column table with 4 rows is titled Equation B. Column 1 is labeled x with entries negative 6, negative 3, 3, 6. Column 2 is labeled y with entries negative 4, negative 2, 2, 4.

The data points for equation A are plotted on the coordinate plane below and are connected by using a straight line.

On a coordinate plane, a line goes through points (negative 5, negative 4), (negative 2, negative 1), (0, 1), (1, 2).

What is the solution to the system of equations?
(–6, –4)
(–5, –4)
(–3, –2)
(0, 1)

PLEASEEEEEE HELP ME ITS DUE TODAY Use a proportion to solve each problem.
1. Tara walks a 2 mile route through her neighborhood for
daily exercise. It takes her 30 minutes. At this rate, how far
can Tara walk in 45 minutes?
2. An infant daycare requires 1 teacher for every 4 children.
How many teachers are required for 20 children?
3. To make purple frosting, you start with white frosting.
Then you add 2 drops of red food coloring and 3 drops of
blue food coloring. If 4 red drops come out with the first
squeeze, how many blue drops should you add?
4. Arlen delivers 28 newspapers each morning. The route takes
him 40 minutes. If his route increases to 35 newspapers, how
long will it take him?
6. On a map, 1 inch represents 50 miles. You measure the
distance on the map between two towns as 3 inches
How many miles apart are the two towns?
6. Kelsey earns $5 walking her neighbors' dogs twice a week.
At this rate, how much should Kelsey cam if she walks the
dogs 6 days each week?
7. Jeff drove the first 200 miles of a trip in 3 hours. At this
rate, how long will the 500 mile trip take, with no stops?
8. Lisa types 6 pages in 36 minutes. Frank types 5 pages in
30 minutes. Do they type at the same rate? Use a proportion
to explain.

what is the quotient 2 1/5 over negative 1/10​

Alyssa is learning to drive her parents' car.
She increases her speed for 20 seconds.
She slows down for 10 seconds.
She stays approximately the same speed for the next 20 seconds.
She then slows down to a stop for the last 5 seconds.
Select the graph that best represents Alyssa's speed over time.

Reggie has 176 pictures of animals. He wants to keep half and then divide the rest equally among four friends. ... How many pictures will each friend get?

Charles has 24 marbles. He has 6 more yellow marbles than blue marbles.
Which equation represents this situation.

The dance team has three cupcake sales a
year to raise money. The amount of money
they make is a function of the amount of
people who buy cupcakes. This function is
represented by the three ordered pairs (40,
100), (70, 175) and (90, 225). What is the
domain of this function?
help

3. Given the equation determine:
f(x)= x² - 4
f(-3)

A scarce gem’s value increases exponentially at 4% per year. If one is worth $5200 this year, when will its value exceed $10000?

Tina's plans to make wooden fences To put heard to triangle art pieces In

How much wood would she need for triangle DFG
​

These points are linear. Find the slope.

In a production process, the probability of manufacturing a defective rear view mirror for a car is 0.075. Assume that the quality status of any rear view mirror produced in this process is independent of the status of any other rear view mirror. A quality control inspector is to examine rear view mirrors one at a time to obtain three defective mirrors. Determine the probability that the third defective mirror is the 10th mirror examined.

vincent has cut three pieces of rope to complete a science project

Literally the last question pls get it right

please help!!!!!! 13 points

Someone please help look at the picture please anything would help

please click to go to my question pleaseeeeeeeee https://brainly.com/question/19665659
click click
plz clickkkkkkkkkkkkkkkk\

Match each multiplication expression with the number of decimal places in its product

PLEASE HELP :( I WILL GIVE BRAINLIEST ANYTHING