Question

PART I

In a consumer research study, several Meijer and Walmart stores were surveyed at random and the average basket price was recorded for each. It was found that the average basket price for 49 Meijer stores was $52.202 with a standard deviation of $11.091. Similarly, 51 Walmart stores had an average basket price of $65.968 with a standard deviation of $14.839. If a 99% confidence interval for the difference between the true average basket prices of Meijer versus Walmart is calculated, what is the margin of error? You can assume that the standard deviations of the two populations are statistically similar.

	1) 6.215
	2) 6.904
	3) 2.6269311
	4) 6.769
	5) 2.6280324

PART II

It is believed that using a solid state drive (SSD) in a computer results in faster boot times when compared to a computer with a traditional hard disk (HDD). You sample 11 computers with an HDD and note a sample average of 31.1 seconds with a standard deviation of 4.6342 seconds. A sample of 10 computers with an SSD show an average of 10.744 seconds with a standard deviation of 1.3808 seconds. Construct a 99% confidence interval for the difference between the true average boot times of the two types of hard drives. Assume the difference will represent (HDD-SSD) and that the population standard deviations are statistically the same.

	1) (5.098, 35.614)
	2) (15.989, 24.723)
	3) We only have the sample means, we need to know the population means in order to calculate a confidence interval.
	4) (16.424, 24.288)
	5) (18.829, 21.883)

PART III

In a packing plant, one of the machines packs jars into a box. A sales rep for a packing machine manufacturer comes into the plant saying that a new machine he is selling will pack the jars faster than the old machine. To test this claim, each machine is timed for how long it takes to pack 10 cartons of jars at randomly chosen times. Given a 95% confidence interval of (-8.73, -2.65) for the true difference in average times to pack the jars (old machine - new machine), what can you conclude from this interval?

	1) We are 95% confident that the average packing time of the new machine is greater than the old machine. The sales rep does not appear to be telling the truth.
	2) There is no significant difference between the average packing times of the two machines. The sales rep does not appear to be telling the truth.
	3) We are 95% confident that the average packing time of the old machine is greater than the new machine. The sales rep appears to be correct.
	4) We are 95% confident that the difference between the two sample means falls within the interval.
	5) We do not have enough information to make a conclusion.

Answer 1

Assume that the population standard deviations are equal.

So we can use here pooled t interval.

Margin of error (E) :

Where SE is standard error

SE = 13.13753 * 0.20004

SE = 2.628032

and tc is t critical value for alpha = 1 - c = 1-0.99 = 0.01 and

degrees of freedom = n1+n2-2 = 49+51 - 2 =98

tc from excel using function:

=TINV(0.01,98)

= 2.627                     (Round to 3 decimal)

tc = 2.627

E = 2.627 * 2.628032

E = 6.904               (Round to 3 decimal)

Margin of error is 6.904