The SAT and the ACT are the two major standardized tests that colleges use to evaluate candidates. Most students take just one of these tests. However, some students take both. The data data187.dat gives the scores of 60 students who did this. How can we relate the two tests?
(a) Plot the data with SAT on the x axis and ACT on the
y axis. Describe the overall pattern and any unusual
observations.
(b) Find the least-squares regression line and draw it on your
plot. Give the results of the significance test for the slope.
(Round your regression slope and intercept to three decimal places,
your test statistic to two decimal places, and your
P-value to four decimal places.)
| ACT = | + (SAT) |
| t = | |
| P = |
(c) What is the correlation between the two tests? (Round your
answer to three decimal places.)
Data Set:
obs sat act 1 805 16 2 757 17 3 731 13 4 1054 23 5 996 17 6 616 11 7 825 14 8 924 18 9 918 21 10 877 20 11 1107 24 12 764 17 13 886 17 14 750 17 15 1393 30 16 670 12 17 775 18 18 1172 26 19 897 20 20 930 22 21 869 21 22 863 20 23 770 14 24 776 20 25 1012 22 26 780 15 27 704 14 28 1055 23 29 791 19 30 910 17 31 1062 22 32 786 18 33 964 18 34 1021 21 35 936 19 36 900 22 37 902 21 38 950 16 39 1005 25 40 794 22 41 843 21 42 1082 25 43 727 18 44 903 16 45 782 16 46 928 25 47 1092 25 48 781 14 49 819 20 50 1066 24 51 982 20 52 1161 27 53 910 17 54 992 23 55 788 17 56 761 15 57 1014 28 58 986 18 59 578 9 60 636 11
In: Statistics and Probability
The SAT and the ACT are the two major standardized tests that colleges use to evaluate candidates. Most students take just one of these tests. However, some students take both. The data data25.dat gives the scores of 60 students who did this. How can we relate the two tests?
(a) Plot the data with SAT on the x axis and ACT on the y axis. Describe the overall pattern and any unusual observations.
(b) Find the least-squares regression line and draw it on your plot. Give the results of the significance test for the slope. (Round your regression slope and intercept to three decimal places, your test statistic to two decimal places, and your P-value to four decimal places.)
ACT = + (SAT)
t =
P =
(c) What is the correlation between the two tests? (Round your answer to three decimal places.)
obs sat act 1 882 19 2 993 21 3 1172 23 4 800 12 5 845 19 6 1015 22 7 862 20 8 860 23 9 635 17 10 962 18 11 1004 26 12 840 15 13 1023 21 14 1134 23 15 642 15 16 920 21 17 842 18 18 820 16 19 889 22 20 815 17 21 570 14 22 1107 24 23 984 21 24 721 20 25 1026 17 26 748 17 27 972 19 28 912 20 29 857 13 30 905 18 31 1076 22 32 1151 26 33 488 12 34 789 13 35 986 21 36 697 17 37 780 17 38 964 25 39 1019 30 40 1003 26 41 666 10 42 1061 25 43 1106 26 44 1151 24 45 705 17 46 1018 27 47 881 20 48 1192 26 49 750 17 50 824 16 51 762 23 52 615 11 53 855 19 54 1022 22 55 1018 23 56 759 18 57 813 21 58 965 22 59 1046 26 60 1018 21
In: Statistics and Probability
Identify the sample chosen for the study.
The number of times 12 out of 27 students on your floor order pizza in a week.
a) all students who order pizza in a week
b) the 27 students on your floor
c) the 12 students on your floor
In: Statistics and Probability
Aluminum reacts with excess hydrochloric acid to form aqueous aluminum chloride and 30.6 mL of hydrogen gas over water at 27°C and 751 mmHg. How many grams of aluminum reacted? The partial pressure of water at 27°C is 26.8 mmHg.
In: Chemistry
Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the 22nd, 27th, 59th, and 69th percentiles. If needed, round your answers to two decimal digits.
| Percentile | Value |
| 22% | |
| 27% | |
| 59% | |
| 69% |
In: Math
Required
Identify the following costs as fixed or variable: Costs related to plane trips between Boston, Massachusetts, and San Diego, California, follow. Pilots are paid on a pertrip basis.
a. Pilots’ salaries relative to the number of trips flown.
b. Depreciation relative to the number of planes in service.
c. Cost of refreshments relative to the number of passengers.
d. Pilots’ salaries relative to the number of passengers on a particular trip.
e. Cost of a maintenance check relative to the number of passengers on a particular trip.
f. Fuel costs relative to the number of trips. Metro National Bank operates several branch offices in grocery stores. Each branch employs a supervisor and two tellers. Costs related to Metro's branch operations follow.
g. Tellers’ salaries relative to the number of tellers in a particular district, which is composed of branches.
h. Supplies cost relative to the number of transactions processed in a particular branch.
i. Tellers’ salaries relative to the number of customers served at a particular branch.
j. Supervisors’ salaries relative to the number of branches operated.
k. Supervisors’ salaries relative to the number of customers served in a particular branch.
l. Facility rental costs relative to the size of customer deposits. Costs related to operating a fastfood restaurant follow.
m. Depreciation of equipment relative to the number of restaurants.
n. Building rental cost relative to the number of customers served in a particular restaurant.
o. Manager’s salary of a particular store relative to the number of employees.
p. Food cost relative to the number of customers.
q. Utility cost relative to the number of restaurants in operation.
r. Company president’s salary relative to the number of restaurants in operation.
s. Land costs relative to the number of hamburgers sold at a particular restaurant.
t. Depreciation of equipment relative to the number of customers served at a particular restaurant.
In: Accounting
Sampling Distribution show all your work for full point.
A bank in a small town has 100,000 customers. A national survey on the banking habits of people in U.S. shows that 80% of the people with income higher than 75,000 dollars have both savings and checking accounts and also shows that the average number of banking operations that a person aged 18 and over performs per week is 10. The manager of the bank decides to do a survey among the customers of his bank and takes a simple random sample of 680 customers aged 18 and over. In the sample, the average number of banking transactions per week is 13 with standard deviation equal to 5.
The average number of times a customer carries out banking transactions per week is_________ give or take _______ or so. Show how you computed your answers.
Give a 90% and a 99% confidence interval for the average number of banking operations per week for the town residents aged 18 and over. What is the difference in Margin of error, how does it affect your confidence interval. Show your working and intepret in plain English
Is the apparent difference in banking habits between the nation and the customers of the bank real or just due to chance? Explain for both 90% and 99% confidence levels.
A 95% confidence interval gives a range of values for the _______which are plausible according to the observed data. Fill in the blanks.
(Possible answer: (A) Population average, (B) Sample average).
The sample standard deviation measures how far _______ is from sample average.
The standard deviation for the sample average measures how far __________is from the population average - for typical __________.
To fill in the blanks, choose among: (A) number of bank operations, (B) average number of operations, (C) samples, (D) customers aged 18 and over, (E) bank, (F) person with high income.
In: Statistics and Probability
| Facts | ||||
| Most flights are scheduled during early morning or early evening. | ||||
| Based on their circumstances passengers can require drastically different amounts of time for check-in. | ||||
| Attendants at the service counters must be able to serve passengers at a higher rate than the arrival rate of those passengers. | ||||
| At some times there are many departing and arriving flights, while at other times there are few flights. | ||||
| Challenge | ||||
| To determine how many service counters to keep open. | ||||
| Busy Period 1 | Busy Period 2 | |||
| Early morning (6:30am to 9:00am) | Early evening (6:00pm to 8:00pm) | |||
| Many departing domestic flights | Many departing international flights | |||
| Average time between consecutive customer arrivals | Average Service Time | |||
| 4 minutes for both the morning and evening | 8 minutes in the morning | |||
| 6 minutes in the middle of the day | 15 minutes in the evening | |||
| 6 minutes in the middle of the day | ||||
| With multiple service counters, customers can be routed through a single line or dedicated lines for each counter. | ||||
| You must ensure that customers are not waiting very long and that you're not wasting resources on open counters. | ||||
| QUESTIONS | ||||
| During each period: | ||||
| What is the number of counters that need to be open? | ||||
| What is the average number of customers in queue and the average waiting time for a customer in the queue before being serviced for check in? | ||||
| When you need multiple counters open: Do you have one queue for all counters? Do you have dedicated queues for each counter? | ||||
| What else is being overlooked in the above scenario and your analysis? | ||||
| How do you ensure that customers are not waiting in line too long before being checked in? | ||||
| How do you ensure that you don't have too many counters open with no customers at these counters? | ||||
In: Operations Management
In: Accounting
Wegmans food stores conducted a study to see how many customers will return to the same store in the future. The study showed that 40% of the customers visiting a specific store will return in the future to the same store. Suppose seven customers are selected at random, what is the probability that:
(a) Exactly four customers will return?
(b) All seven customers will return?
(c) At least six customers will return?
(d) At least one customer will return?
(e) How many customers would be expected to return to the same store?
In: Statistics and Probability