Question

1)Restaurants can be classfied as "full service" or quick service. Full service restaurants seat customers at a table that is assigned to a server who takes the customers order.the customer recieves service throughout the meal and pays after eating.Chilis,the olive garden, and the outback steakhouse are examples of full service restaurants. quick- service restaurants sell fast food.customers pay for their meals before eating at a cash resgiter or kiosk, there are no waiters assigned to tables, and limited or no service is provided during the meal. taco bell and chick fil a are examples of quick service restaurants.

A houston area restaurant analyst wants to see if there is a difference between full service and quick service restaurants in the mean number of years of experience that their general managers have in the industry total. after sending out a survery to hundreds of restaurants in the houston area, she obtained the following data:

GROUP MEAN STANDARD DEVIATION n

full service group (1) 16.7 3.9 147

quick serviice group (2) 14.8 4.6 93

A) calculate a 90% confidence interval for the difference in mean years of experience between full-service and quick service managers.USE THE FACT THAT THE DEGREES OF FREEDOM V=172.5 SHOW ALL WORK

B)INTERET the interval you calculated in (A) in the context of the problem statement refer specificially to the situation described in the problem statement and the specific group names.Use template.

The researcher can be ________% confident that the true _________ between __________and __________ is between__________and_________.

C) Using your answers to (B) can the researcher conclude that the two types of managers differ in mean years of experience and WHY? BE SPECIFIC

D) The researcher now wants to see if there is a difference in the proportion of managers of full service and quic service restaurants who have at least a bacholors degree (coded as "bachelors + " in the table below) data from the same study is shown below

Group Bachelor's associates or lower total

full service (group 1) 71 76 147

quick service (group 2) 35 58 93

find a 99% confidence interval for the difference in the proportion of managers of full service and quick restaurants who have bachelors or higher.

E) using your answer to (D) can the researcher caonclude that the two types of managers differ in educastion level? explain why

Answer 1

Let fs be the full-service group and qs be the quick service group.

Given,

x_fs = 16.7

s1 = 3.9

n1 = 147

x_qs = 14.8

s2 = 4.6

n2 = 93

Null and Alternate Hypothesis:

H0: µ_fs - µ_qs = 0

Ha: µ_fs - µ_qs > 0

Alpha = 0.05

Test Statistic (t) = (x_{fs ­­}– x_{qs ­}– ( µ_fs - µ_qs ))/(s₁²/n₁ + s₂²/n₂)^1/2 = 3.30

Given to use df = 172.5

p-value = TDIST(3.3,172.5,1) = 0.000588

Since, the p-value is less than 0.05, we reject the null hypothesis in favour of alternate hypothesis.

A)

90% CI for difference of Mean

Zcritical = 1.64

CI = x_{fs ­­}– x_qs +/- Z_critical * (s₁²/n₁ + s₂²/n₂)^1/2 = (0.96,2.84)

B)

The researcher can be 90% confident that the true mean difference between full-service group and quick-service group is between 0.96 and 2.84.

C)

Yes, the two types of managers differ in their mean years of experience because the test statistic is outside the 90% confidence interval.

D)

full service (group 1) 71 76 147

quick service (group 2) 35 58 93

99% CI for difference of Mean

Zcritical = 2.58

CI = x_{fs ­­}– x_qs +/- Z_critical * (s₁²/n₁ + s₂²/n₂)^1/2 = (13.59,58.41)

E)

Test Statistic = 4.14

Since the test statistic is in the 99% confidence interval, hence the two types of managers do not differ in education level.