A. Suppose we test the proportions of people who like having a cup of coffee early in the morning for two populations: H0 : p1= p2 vs Ha : p1< p2. The sample sizes for these two population are n1= n2=400 and the numbers of people who like coffee are x1 =160 and x2=200 respectively. What is the value of the test statistics?

a. -2.8571        b. -2.8427

c. -2.8866        d. -2.8284

B. Suppose we take Type I error level to be α = 0.01 in the above population proportion testing. What is your conclusion?

a. Reject H0.   b. Accept H0 c. Do not know.

Suppose I have a 99% confidence interval of 6±2. Someone says, “Hey! I think µ = 3!” What should I say to them?

A. I am 100% sure that you are wrong, because µ = 6.

B. I am 99% sure that you are right.

C. I am 99% sure that µ is between 4 and 8.

D. I am 100% sure that µ ≠ 3.

2. (25pts) The decrease in cholesterol level after eating a certain brand of oatmeal for breakfast for one month in people with cholesterol levels is Normally distributed. A random sample of 25 adults was selected and mean 8.5 and standard deviation 3. The brand advertises that eating its oatmeal for breakfast daily for one month will produce a mean decrease in cholesterol of more than 10 units for people with cholesterol levels. (α= 0.05)

c. Report a 95% one-sided confidence interval for the mean decrease in cholesterol.

d. What is the power of the test?

What is the relationship between the attendance at a major league ball game and the total number of runs scored? Attendance figures (in thousands) and the runs scored for 11 randomly selected games are shown below.

Attendance4135464445201310573315

Runs6411910354851

Find the correlation coefficient: r=r=    Round to 2 decimal places.

The null and alternative hypotheses for correlation are:
H0:H0: ? μ r ρ  == 0
H1:H1: ? r μ ρ   ≠≠ 0
The p-value is:    (Round to four decimal places)

Use a level of significance of α=0.05α=0.05 to state the conclusion of the hypothesis test in the context of the study.

There is statistically significant evidence to conclude that there is a correlation between the attendance of baseball games and the runs scored. Thus, the regression line is useful.

There is statistically significant evidence to conclude that a game with a higher attendance will have more runs scored than a game with lower attendance.

There is statistically insignificant evidence to conclude that there is a correlation between the attendance of baseball games and the runs scored. Thus, the use of the regression line is not appropriate.

There is statistically significant evidence to conclude that a game with higher attendance will have fewer runs scored than a game with lower attendance.

r2r2 =  (Round to two decimal places) (Round to two decimal places)

Interpret r2r2 :

Given any fixed attendance, 61% of all of those games will have the predicted number of runs scored.

There is a 61% chance that the regression line will be a good predictor for the runs scored based on the attendance of the game.

61% of all games will have the average number of runs scored.

There is a large variation in the runs scored in baseball games, but if you only look at games with a fixed attendance, this variation on average is reduced by 61%.

The equation of the linear regression line is:   
ˆyy^ =  + xx   (Please show your answers to two decimal places)

Use the model to predict the runs scored at a game that has an attendance of 25,000 people.
Runs scored =  (Please round your answer to the nearest whole number.)

Interpret the slope of the regression line in the context of the question:

The slope has no practical meaning since the total number runs scored in a game must be positive.

For every additional thousand people who attend a game, there tends to be an average increase of 0.15 runs scored.

As x goes up, y goes up.

Interpret the y-intercept in the context of the question:

The y-intercept has no practical meaning for this study.

The average runs scored is predicted to be 1.

If the attendance of a baseball game is 0, then 1 runs will be scored.

The best prediction for a game with 0 attendance is that there will be 1 runs scored.

Code needed in C++, make changes to the file provided (18-1, has 3 files)

Chapter 18 Stacks and Queues

-----------------------------------------------------------------------------------------------------

capacity is just 5

1. push 6 numbers on the stack

2. catch the overflow error in a catch block

3. pop one element, which means your capacity is now down to 4

4. push the element that was rejected earlier

5. verify your entire stack by popping to show the new numbers.

IntStack.h

#include <memory>

using namespace std;

class IntStack

{

unique_ptr<int[]>stackArray;

int capacity;

int top;

public:

// Constructor

IntStack(int capacity);

// Member functions

void push(int value);

void pop(int &value);

bool isEmpty() const;

// Stack Exceptions

class Overflow {};

class Underflow {};

};

IntStack.cpp

ZOOM

#include "intstack.h"

//************************************

// Constructor *

//************************************

IntStack::IntStack(int capacity)

{

stackArray = make_unique<int[]>(capacity);

this->capacity = capacity;

top = 0;

}

//***********************************

// Adds a value to the stack *

//***********************************

void IntStack::push(int value)

{

if (top == capacity) throw IntStack::Overflow();

stackArray[top] = value;

top++;

}

//****************************************

// Determines whether the stack is empty *

//****************************************

bool IntStack::isEmpty() const

{

return top == 0;

}

//************************************************

// Removes a value from the stack and returns it *

//************************************************

void IntStack::pop(int &value)

{

if (isEmpty()) throw IntStack::Underflow();

top--;

value = stackArray[top];

}

pr18-01.cpp

// This program illustrates the IntStack class.

#include "intstack.h"

#include <iostream>

using namespace std;

int main()

{

IntStack stack(5);

int values[] = { 5, 10, 15, 20, 25 };

int value;

cout << "Pushing...\n";

for (int k = 0; k < 5; k++)

{

cout << values[k] << " ";

stack.push(values[k]);

}

cout << "\nPopping...\n";

while (!stack.isEmpty())

{

stack.pop(value);

cout << value << " ";

}

cout << endl;

return 0;

}

You plan on exposing 9 strains of bacteria (labelled A - I) to a mutagen. You hypothesize that mutagen A induces more mutations than mutagen B. Following each exposure, you count the mutations observed in the genome compare to the wild strain genotype. Figure out what kind of statistical test would be appropriate for this study.

Number mutations observed in genome
Mutation    A B    C    D E    F    G H I
Mutagen A 52 17 45 40 20 30 10    15    41

Mutagen B 59 15 63 40 17 45 32 20 40

What is your null and alternate hypothesis?  What are your statistical results?  Should you reject, or fail to reject, your null hypothesis? Why?

Show all work for credit (Include original formulas, hypotheses, rejection criteria, decision, and statement in context).

A comparative study of four methods for treating hyperactivity in children was performed in 16 children.  After the treatment, hyperactivity was scored on a scale of 1 to 100 where 100 is high hyperactivity.  With 99% confidence is there a statistically significant difference among hyperactivity treatments?

10 points -Write the null and alternate hypotheses:

Null hypothesis: ________m₁=m₂=m₃=m₄______________________________________________________________________________

Alternate Hypothesis: _______differences in the means____________________________________

80 points - Fill in the chart.  Show your work for each intermediate calculation.  (Staple your work to this page.)

10 points -Are you able to reject the null hypothesis?  Show work.  Summarize your conclusion.  

1. Use the following information for the next four problems. A researcher is interested in estimating the mean salary of public school teachers in a particular region. A random sample of 9 teachers is selected and the salary of each one is recorded. The researcher calculates a sample mean of $45,000 and a sample standard deviation of $1,600. Assume that the salaries in the population vary according to a normal distribution.

   The mean salary of all public school teachers in the region is a __________ while the sample mean $45,000 is a __________.

   	a.	parameter, statistic
   	b.	statistic, parameter
   	c.	parameter, parameter
   	d.	statistic, statistic

2. Calculate a 95% confidence interval to estimate the mean salary.

   	a.	$45,000  $348.44
   	b.	$45,000  $1,206.40
   	c.	$45,000  $1,229.87
   	d.	$45,000  $1,045.33

1. Suppose, instead, that a larger sample of teachers had been selected while still using the 95% confidence level. The new confidence interval, based on the larger sample, would be __________ the interval in the previous problem.

   	a.	shorter than
   	b.	the same length as
   	c.	longer than

1. Out of 200 people sampled, 92 had kids. Based on this, construct a 99% confidence interval for the true population proportion of people with kids.

Give your answers as decimals, to four places

2.

A fitness center is interested in finding a 98% confidence interval for the mean number of days per week that Americans who are members of a fitness club go to their fitness center. Records of 261 members were looked at and their mean number of visits per week was 3.5 and the standard deviation was 1.7. Round answers to 3 decimal places where possible.

a. To compute the confidence interval use a ? z t  distribution.

b. With 98% confidence the population mean number of visits per week is between  and   visits.

c. If many groups of 261 randomly selected members are studied, then a different confidence interval would be produced from each group. About  percent of these confidence intervals will contain the true population mean number of visits per week and about  percent will not contain the true population mean number of visits per week.

The following random sample was selected from a normal distribution: 4, 6, 3, 5, 9, 3.

a. Construct a 90% confidence interval for the population mean.

b. Construct a 95% confidence interval for the population mean.

c. Construct a 99% confidence interval for the population mean.

d. Assume that the sample mean x and sample standard deviation s remain exactly the same as those you just calculated but are based on a sample of n = 25 observations rather than n = 6 observations. Repeat parts a–c. What is the effect of increasing the sample size on the width of the confidence intervals?

e. Use Rejection region to test the null hypothesis that the mean of the population is 6 against the alternative hypothesis, ?<6. Use ? = .05.

f. Use p-Value to test the null hypothesis that the mean of the population is 6 against the alternative hypothesis, ? ≠6. Use ? = .05.

Assume that 40% of graduates come from University A and and earn salaries of 30,000 on average with a standard deviation of 5,000. The remainder come from University B and earn salaries of 25,000 on average with a standard deviation of 7,500. If you are told that a graduate is earning less than 35,000, what is the probability that they came from University A? (Assume salaries are normally distributed.)

A makeup test is given and the average (μX) score out of 100 was 85.0, with a SD (σX) of 3.0. Assuming a normal distribution, find the dividing line (test scores) between the A's, B's, C's, D's, and E's. This time the highest 6% will be the A's, the next 16% B's, the next 26% C's, the next 36% D's.

Given the data below, what is the upper control limit for the Moving Range control chart? Please enter your answer with at least 4 significant digits.

Data:

A test is given and the average (μX) score out of 100 was only a 53.1, with a SD (σX) of 8.9. Assuming the grades followed a normal distribution, use the Z table or Excel and formulas to find the dividing line (test scores) between the A's, B's, C's, D's, and E's. Starting from the top, the teacher will give the highest 15% A's, the next 10% B's, the next 30% C's, the next 25% D's, and the bottom 20% will receive E's.

Consider the following data to be used in a regression. xi yi 1 0 2 10 3 25 4 30 5 35 (a) Find the values of b0 and b1. (b) Find the Coefficient of Determination. (c) Find the estimated standard deviation of b1 and the corresponding t-statistic. At the 1% level of significance, can you reject the null hypothesis? Make sure you state the null and alternative hypotheses. (d) Find the F-statistic. Is the equation significant at the 1% level? Make sure you state the null and alternative hypotheses. Use the p-value approach.