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.

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  

Step-by-step explanation:

From the question we are told that

    The sample size is  n  =  36

    The first sample mean is  

    The first standard deviation is  

    The second sample mean is  

     The second standard deviation is  

      The level of significance is  

The null hypothesis is  

The alternative hypothesis is

Generally the test statistics is mathematically represented as

=>    

=>    

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

=>    

=>    

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    

=>  

Generally from the normal distribution table the critical value  of   is  

Generally the margin of error is mathematically represented as  

 =>

  =>

Generally 95% confidence interval is mathematically represented as  

=>  

=>  

she drove 134 miles

step-by-step explanation: