The fire department tested two types of fire extinguishers on gasoline fires. They set 10 gallons of gasoline ablaze and then timed how long it took to extinguish the blaze using one extinguisher. The process was repeated 6 times for two types of fire extinguishers (Type 1 and Type 2). Assuming the population variances are equal: a) Use a 5% significance interval to test the claim that it takes longer to put out the fire using a Type 2 fire extinguisher (I finished this problem correctly I believe. I attached a photo of my work). b) Form a 90% confidence interbal for for the difference of the true means in the time needed to put out a fire using two fire extinguishers TYPE N MEAN STD. DEVIATION STD. ERROR MEAN Type 1 6 12.8333 1.47196 0.60093 Type 2 6 15.3333 4.32049 1.7638

a)

And the deviation would be just the square root of the variance:

And now we can calculate the statistic:

Now we can calculate the degrees of freedom given by:

And now we can calculate the p value using the altenative hypothesis:

If we compare the p value obtained and using the significance level assumed we have so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.    

b)

And replacing we got:

Step-by-step explanation:

Part a

TYPENMEANSTD. DEVIATIONSTD. ERROR MEAN

Type 1612.8333         1.47196              0.60093

Type 2615.3333         4.32049               1.7638

When we have two independent samples from two normal distributions with equal variances we are assuming that  

And the statistic is given by this formula:

Where t follows a t distribution with degrees of freedom and the pooled variance is given by this formula:

This last one is an unbiased estimator of the common variance

The system of hypothesis on this case are:

Null hypothesis:

Alternative hypothesis:

Or equivalently:

Null hypothesis:

Alternative hypothesis:

Our notation on this case :

represent the sample size for group 1

represent the sample size for group 2

represent the sample mean for the group 1

represent the sample mean for the group 2

represent the sample standard deviation for group 1

represent the sample standard deviation for group 2

First we can begin finding the pooled variance:

And the deviation would be just the square root of the variance:

And now we can calculate the statistic:

Now we can calculate the degrees of freedom given by:

And now we can calculate the p value using the altenative hypothesis:

If we compare the p value obtained and using the significance level assumed we have so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.    

Part b

For the confidence interval we know that the confidence is 90% so then the value os and , the degrees of freedom are given by:

And the crtitical value for this case would be

The confidence interval for the difference of means is given by:

And replacing we got:

is this part of a question or something

quit

step-by-step explanation: