2. Notation for comparing two populations

Suppose in an effort to manage her inventory levels better, the owner of two steak and seafood restaurants, both located in the same city, hires a statistician to conduct a statistical study. The owner is interested in whether the restaurant located on the east side sells more filets mignons per night than the restaurant located on the west side of the city. The statistician selects a random sample of 102 nights that the east-side restaurant is open. The mean number of filets mignons sold per night at the east-side location is 15.3 with a sample standard deviation of 0.4. Likewise, the mean number of filets mignons sold per night at the random sample of 83 nights that the west-side restaurant is open is 16.8 with a sample standard deviation of 5.5.

Suppose you intend to conduct a hypothesis test on the difference in population means. In preparation, you identify the sample of nights at the east restaurant as sample 1 and the sample of nights at the west restaurant as sample 2. Organize the provided data by completing the following table:

Sample 1	Sample 2
N1

=

N2

=

1

=

2

=

X1

=

X2

=

1

=

2

=

s1

=

s2

=

The difference in sample means for sample 1 and sample 2 is .

The estimate of the standard deviation of the sampling distribution of the differences in sample means, s(XX)

, is .

Now, you know all that you need to know to answer the question about whether the restaurant located on the east side sells more filets mignons per night than the restaurant located on the west side of the city.