Miles per Gallon. The following stem-leaf plot is representing the number of miles per gallon achieved on the highway for 2013 small car models. Construct an Ogive of data by first construction a cumulative frequency table with class width of five. Include: Limits, frequency, and cumulative frequency.

A government researcher is analyzing the relationship between retail sales (in $ millions) and the gross national product (GNP in $ billions). He also wonders whether there are significant differences in retail sales related to the quarters of the year. He collects 10 years of quarterly data. A portion is shown in the accompanying table. Retail sales (in millions) GNP (in billions) d1 d2 d3 2000 1 696048 9740.5 1 0 0 2 753211 9983.5 0 1 0 3 746875 10048.0 0 0 1 4 792622 10184.9 0 0 0 2001 1 704757 10206.2 1 0 0 2 779011 10350.9 0 1 0 3 756128 10332.2 0 0 1 4 827829 10463.1 0 0 0 2002 1 717302 10549.7 1 0 0 2 790486 10634.7 0 1 0 3 792657 10749.1 0 0 1 4 833877 10832.2 0 0 0 2003 1 741233 10940.2 1 0 0 2 819940 11073.6 0 1 0 3 831222 11321.2 0 0 1 4 875437 11508.3 0 0 0 2004 1 795916 11707.8 1 0 0 2 871970 11864.2 0 1 0 3 873695 12047.3 0 0 1 4 938213 12216.6 0 0 0 2005 1 836952 12486.3 1 0 0 2 932713 12613.0 0 1 0 3 940880 12848.7 0 0 1 4 987085 12994.1 0 0 0 2006 1 897180 13264.0 1 0 0 2 987406 13423.3 0 1 0 3 978211 13514.8 0 0 1 4 1018775 13683.2 0 0 0 2007 1 923997 13859.8 1 0 0 2 1016136 14087.6 0 1 0 3 1002312 14302.9 0 0 1 4 1062803 14489.9 0 0 0 2008 1 953358 14520.7 1 0 0 2 1032919 14647.3 0 1 0 3 1006551 14689.2 0 0 1 4 966329 14317.2 0 0 0 2009 1 839625 14172.2 1 0 0 2 919646 14164.2 0 1 0 3 926265 14281.9 0 0 1 4 985649 14442.8 0 0 0

a. Estimate y = β0 + β1x + β2d1 + β3d2 + β4d3 where y is retail sales, x is GNP, d1 is a dummy variable that equals 1 if quarter 1 and 0 otherwise, d2 is a dummy variable that equals 1 if quarter 2 and 0 otherwise, and d3 is a dummy variable that equals 1 if quarter 3 and 0 otherwise. Here the reference category is quarter 4. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

d-1. Reformulate the model to determine, at the 5% significance level, if sales differ between quarter 2 and quarter 3. Your model must account for all quarters. Use quarter 3 as the reference category. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

Data on 72 randomly selected flights departing from the three major NYC airports in 2013.

Departure delays in minutes. Negative times represent early departures.

Q1. We want to estimate the proportion of flights that departed from the NYC airports in 2013 which are delayed. There are two ways we can do this. We can either obtain a point estimate or calculate an interval estimate. Provide estimates using both methods. Use a 99% confidence level. Show all working, define variables and state the distribution as needed.

ANOVA

For the data below -

1. Write H₀ (1 point)
2. Write H₁ (1 point)
3. Compute and report the F statistic ANOVA (using Excel); use (α = .05) - ANOVA (single factor); hint also compute descriptive statistics to help with d6 (2 points)
4. Retain or reject H₀ (1 point)

Find the second minimum of an integer array?

//this is the template we follow. Answer must run in linear time (i.e. no nested loops).

package findsecondminimumtest;

import java.util.Arrays;
import java.util.NoSuchElementException;

public class FindSecondMinimumTest {

/**
* Find the second minimum of an integer array
*
* @param a is the array
* @return the second minimum if array has at least two elements and it
* indeed has a second minimum. If array length is less than two, it throws
* IllegalArgumentException. If there is no second minimum (eg. if your
* array if {1, 1, 1}, there is no second minimum), method throws
* NoSuchElementException.
*/
static int findSecondMin(int[] a) {
// write your code here
int smin = 0;
  return smin;
}

public static void main(String[] args) {
/*
DO NOT CHANGE ANYTHING in the main method!!!. If your code works, properly,
it should print true for all cases except the last two. Last two check for exception case.
It is not hard to understand why it works that way.
*/
int[] a1 = {1, 3, 2, 1}; // 2
int[] a2 = {1, 3, 2}; // 2
int[] a3 = {1, 2, 1, 2}; // 2
int[] a4 = {3, 6, 5, 8, 10, 20, 15}; // 5
int[] a5 = {1, 1, 2, 3, 4, 4}; // 2
int[] a6 = {1, 4, 10, 4, 2}; // 2
int[] a7 = {10, 1, 2, 3, 4, 5}; // 2
int[] a8 = {1, 1, 1, 2, 3}; // 2
int[] a9 = {0, -2, 5, 6}; // 0
int[] a10 = {1, 2, 3, 4, 5, 3, 5, 6}; // 2
int[] a11 = {40, 50, 60, 10, 20, 30}; // 20
int[] a13 = {1, 2, 5, 3, 5}; // 2
int[] a14 = {1, 2, 5, 5, 5}; // 2
int[] a15 = {10, 1, 2, 3, 4, 5, 6, 1}; // 2
int[] a16 = {1, 2, 3, 4, 3, 6}; // 2
int[] a17 = {1, 2, 3, 4, 99, 5, 6}; // 2
int[] a18 = {123, -17, -5, 1, 2, 3, 12, 43, 45}; // -5
int[] a19 = {3, 5, 67, 98, 3}; // 5
int[] a12 = {1, 1, 1}; // Should throw NoSuchElementException exception
int[] a20 = {1}; // Should throw IllegalArgumentException

System.out.println(Arrays.toString(a1) + ": " + (findSecondMin(a1) == 2));
System.out.println(Arrays.toString(a2) + ": " + (findSecondMin(a2) == 2));
System.out.println(Arrays.toString(a3) + ": " + (findSecondMin(a3) == 2));
System.out.println(Arrays.toString(a4) + ": " + (findSecondMin(a4) == 5));
System.out.println(Arrays.toString(a5) + ": " + (findSecondMin(a5) == 2));
System.out.println(Arrays.toString(a6) + ": " + (findSecondMin(a6) == 2));
System.out.println(Arrays.toString(a7) + ": " + (findSecondMin(a7) == 2));
System.out.println(Arrays.toString(a8) + ": " + (findSecondMin(a8) == 2));
System.out.println(Arrays.toString(a9) + ": " + (findSecondMin(a9) == 0));
System.out.println(Arrays.toString(a10) + ": " + (findSecondMin(a10) == 2));
System.out.println(Arrays.toString(a11) + ": " + (findSecondMin(a11) == 20));
System.out.println(Arrays.toString(a13) + ": " + (findSecondMin(a13) == 2));
System.out.println(Arrays.toString(a14) + ": " + (findSecondMin(a14) == 2));
System.out.println(Arrays.toString(a15) + ": " + (findSecondMin(a15) == 2));
System.out.println(Arrays.toString(a16) + ": " + (findSecondMin(a16) == 2));
System.out.println(Arrays.toString(a17) + ": " + (findSecondMin(a17) == 2));
System.out.println(Arrays.toString(a18) + ": " + (findSecondMin(a18) == -5));
System.out.println(Arrays.toString(a19) + ": " + (findSecondMin(a19) == 5));
try {
System.out.println(Arrays.toString(a12) + ": " + (findSecondMin(a12) == 1));
} catch (Exception e) {
System.out.println(e.toString());
}

try {
System.out.println(Arrays.toString(a20) + ": " + (findSecondMin(a20) == 1));
} catch (Exception e) {
System.out.println(e.toString());
}
}

}

Given are five observations for two variables,  and . Use Table 2 of Appendix B.

Round your answers to two decimal places.

a. Using the following equation:

Sy*=s*SQRT(1/n + (x*-xbar)^2/Sigma(xi-xbar)^2)

Estimate the standard deviation of ^y* when x=4 .

b. Using the following expression:

^y*+-(t a/2)Sy*

Develop a  confidence interval for the expected value of y when x=4 .
to

c. Using the following equation:

S pred=s*sqrt(1+1/n+(x*-xbar)^2/sigma(xi-xbar)2

Estimate the standard deviation of an individual value of 7 when x=4.

d. Using the following expression:

^y*=t a/2(S pred)

Develop a  prediction interval for y when x=4

Ideal gas with Cp=32

State 1 (P=1bar T=300 k) compressed isothermally volume becomes 1/2 (state 2),

State 3 gas is compressed adiabatic to P₃=4 bar,

State 4 ideal gas is expanded isothermally to unknown P₄.

Finally gas is compresses back to stage 1.

Fill the blanks in the table for both T and P in all states showing your work

Determine the next number in the sequence: a) 1/4. 4/9. 3/5. 8/11. 5/6. 1/32.

b) How is the relation of the sequence in "a)" different from: 1. 4. 11. 29. 76. 199.

Question 1. A company is planning to purchase a new machine to expand its production. There are two brand available A and B in the market. Both the machines are costing OMR 10000. The following cash inflows are expected to come for both the machines.

Calculate Pay back period and Discounted Payback period for Machine A and Machine B and comment on which machine is better using the two techniques. The discount rate is 3.05%.

Solution: Payback period

Solution: Discounted Payback period

Find whether the following transitions (specified in terms of the initial and final quantum numbers n, ?, m_?, and m_s) are allowed, and if they are, find the energy involved and whether the photon is absorbed or emitted for the hydrogen atom.

(a) (5, 2, -1, 1/2 ) ? (6, 3, -1, 1/2)

Is the transition allowed?
---Select--- Yes or No

What is the energy involved? (Include sign. Enter "none" if the transition is forbidden.)
eV

Is the photon absorbed or emitted?
---Select--- absorbed, emitted, neither, or transition forbidden

(b) (4, 3, 0, 1/2) ? (4, 2, -1, -1/2)

Is the transition allowed?
---Select--- Yes or No

What is the energy involved? (Include sign. Enter "none" if the transition is forbidden.)
eV

Is the photon absorbed or emitted?
---Select--- absorbed, emitted, neither, or transition forbidden

(c) (4, 3, 0, 1/2) ? (3, 4, -2, -1/2)

Is the transition allowed?
---Select--- Yes or No

What is the energy involved? (Include sign. Enter "none" if the transition is forbidden.)
eV

Is the photon absorbed or emitted?
---Select--- absorbed, emitted, neither, or transition forbidden

(d) (2, 1, 0, -1/2) ? (3, 2, 1, -1/2)

Is the transition allowed?
---Select--- Yes or No

What is the energy involved? (Include sign. Enter "none" if the transition is forbidden.)
eV

Is the photon absorbed or emitted?
---Select--- absorbed, emitted, neither, or transition forbidden