Location is known to affect the number, of a particular item, sold by heb pantry. two different locations, a and b, are selected on an experimental basis. location a was observed for 18 days and location b was observed for 13 days. the number of the particular items sold per day was recorded for each location. on average, location a sold 39 of these items with a sample standard deviation of 8 and location b sold 49 of these items with a sample standard deviation of 4. select a 99% confidence interval for the difference in the true means of items sold at location a and b. a) o [-1242,-7582]

b) o132.76, 45.24]

c)。8 1.76, 94.24]

d) 0-1 6.03,-3.97]

e)。[42.76, 55.24]

f. none of the above

d) [-16.03,-3.97]

.

Step-by-step explanation:

Notation and previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

represent the sample of A

represent the sample of B

represent the mean sample  for A

represent the mean sample for B  

represent the sample deviation for A

represent the sample deviation for B

represent the significance level

Confidence =99% or 0.99

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

(1)  

The point of estimate for is just given by:  

The appropiate degrees of freedom are

Since the Confidence is 0.99 or 99%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,29)".And we see that  

The standard error is given by the following formula:  

And replacing we have:  

Confidence interval  

Now we have everything in order to replace into formula (1):  

So on this case the 99% confidence interval for the differences of means would be given by .

d) [-16.03,-3.97]

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

-1/2 +2

step-by-step explanation: