1. Write the regression equation.
2. Discuss the statistical significance of the model as a whole using the appropriate regression statistic at a 95% level of confidence.
3. Discuss the statistical significance of the coefficient for each independent variable using the appropriate regression statistics at a 95% level of confidence.
4. Discuss the statistical significance of the coefficient for each independent variable using the appropriate regression statistics at a 99% level of confidence.
5. What percentage of the observed variation in income is explained by the model?
6. Determine the predicted income of a person who is 50 years old, with 22 years of education, 1 additional family member earning income and works 45 hours per week.    

1) Let   x be a continuous random variable that follows a normal distribution with a mean of 321 and a standard deviation of 41.

(a) Find the value of   x > 321 so that the area under the normal curve from 321 to x is 0.2224.

Round your answer to the nearest integer.
The value of   x is_______

(b) Find the value of x so that the area under the normal curve to the right of x is 0.3745.

Round your answer to the nearest integer.
The value of   x is ______

2) A study has shown that 24% of all college textbooks have a price of $80 or higher. It is known that the standard deviation of the prices of all college textbooks is $10.00. Suppose the prices of all college textbooks have a normal distribution. What is the mean price of all college textbooks?

Round your answer to the nearest integer.

μ=

3) Use a table, calculator, or computer to find the specified area under a standard normal curve.

Round your answers to 4 decimal places.

a) More than a z-score of 2.48; area = _____________

b) More than a z-score of 1.7; area =_____________

c) More than a z-score of -0.41; area = _____________

d) More than a z-score of 00; area = _____________

4)

The highway police in a certain state are using aerial surveillance to control speeding on a highway with a posted speed limit of 55 miles per hour. Police officers watch cars from helicopters above a straight segment of this highway that has large marks painted on the pavement at  1-mile intervals. After the police officers observe how long a car takes to cover the mile, a computer estimates that cars speed. Assume that the errors of these estimates are normally distributed with a mean of  0 and a standard deviation of  3.58 miles per hour.

a. The state police chief has directed his officers not to issue a speeding citation unless the aerial units estimate of speed is at least 66 miles per hour. What is the probability that a car travelling at 61 miles per hour or slower will be cited for speeding?

Round your answer to four decimal places.

The probability that a car travelling at 61 miles per hour or slower will be cited for speeding is ______

b. Suppose the chief does not want his officers to cite a car for speeding unless they are 99% sure that it is travelling at 61 miles per hour or faster. What is the minimum estimate of speed at which a car should be cited for speeding?

Round your answer to the nearest integer.

The minimum estimate of speed is __

In polynomial regression, what assumptions underlie the (strict) validity of the various p-values and confidence intervals?

9.9. Is gender independent of education level? A random sample of people were surveyed and

each person was asked to report the highest education level they obtained. Perform a hypothesis

test. Include all 5 steps.

A 9 monthold boy is insulin dependent diabetes mellitus (DDM) was seen in a pediatric diabetic clinic in London. He was well and had no gastrointestical symptoms. He was screened for antibodies. The screening test has a sensitivity of .93 and specificity of .90. The prevalence is 4.5 It was estimated that the patient.s CD willo be 4.5%. What will his post test probability be?

An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 4.2 4.2 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 240 240 engines and the mean pressure was 4.3 4.3 pounds/square inch. Assume the variance is known to be 0.64 0.64 . A level of significance of 0.02 0.02 will be used. Determine the decision rule. Enter the decision rule.

Irena Blazes, the fire chief of Flares, Oregon, wants to introduce volunteers into the department but fears that employees will resist volunteers. Chief Blazes would like to use volunteers and wants to avoid potential labor problems. She has decided to introduce volunteers if 60 percent of the employees agree to work with them. She administers a survey to all 150 paid firefighters, and 90 respond. Among these 90 firefighters, 62 say that they agree to work with volunteers and accept them in the work place. Given the results of this survey, should Chief Blazes procced with her plans to introduce volunteer firefighters? What is the probability that she could obtain the survey results if 60% or fewer of the paid firefighters were willing to accept volunteers?

Please note that for all problems in this course, the standard cut-off (alpha) for a test of significance will be .05, and you always report the exact power unless SPSS output states p=.000 (you’d report p<.001). Also, remember when hand-calculating, always use TWO decimal places so that deductions in grading won’t be due to rounding differences.

In each scenario below, specify each variable as a response variable, an explanatory variable, or neither. Explain your choices.

a. A climatologist wishes to predict future monthly rainfall in Los Angeles. To inform his predictive model, for each month of the past 30 years, he records the name of the month (Jan.-Dec.), total rainfall (mm), and the Oceanic Niño Index (a measure of sea surface temperature differences, in ºC).

b. A researcher conducts an experiment in a residence for senior citizens to investigate the effect of floor type on the risk of fall-related injury. For each individual in the facility, she records the type of flooring (either standard flooring or a new, rubber flooring that absorbs the impact of falls) in their room, their age, and the number of fall-related injuries that they sustained over the previous two years. my question : are the age and the number of fall related injuries over the previous two year also the explanatory variables?

c. A medical researcher studies a group of boys, recording the age at which they reach puberty (years) and their BMI (kg/m2) at that time. Her goal is to quantify the association between these two variables.

My answer: is this correct?

a. Explanatory variable : records the name of the month (Jan.-Dec.), the Oceanic Niño Index (a measure of sea surface temperature differences, in ºC)

Response variable: total rainfall (mm),

b.Explanatory variable: the type of flooring (either standard flooring or a new, rubber flooring that absorbs the impact of falls) in their room, their age, the number of fall-related injuries that they sustained over the previous two years.

c. Neither: the age at which they reach puberty (years) and their BMI (kg/m2) at that time

Suppose that 45 studentsare applying to a company. There are 5 job openings but 8 offers are made because typically a few students will turn down the job. Each student has a 60% chance of accepting a job offer, independent of the other student’s decisions. What is the CDF for the number of students who accept job offers?

please show me the method and the answer

Write down and explain in words and/or graphs the five Multiple Linear Regression (MLR) assumptions.

3. The time T required to receive a message at node B from node A is an exponentially distributed random variable with mean 1/10 (milliseconds). The time T is measured from the moment that a message left node A to the moment that it was received by node B.

a) What is the probability that T exceeds 105 milliseconds?

b) What is the probability that a message is received after 200 milliseconds given that no message was received before 95 milliseconds? That is, calculate: P(T > 200 | T 95):

A study reports that 36% of companies in Country A have three or more female board directors. Suppose you select a random sample of 100 respondents. Complete parts​ (a) through​ (c) below.

a. What is the probability that the sample will have between 33​% and 43​% of companies in Country A that have three or more female board​ directors?

b. The probability is 70​% that the sample percentage of Country A companies having three or more female board directors will be contained within what symmetrical limits of the population​ percentage?

c. The probability is 99.7​% that the sample percentage of Country A companies having three or more female board directors will be contained within what symmetrical limits of the population​ percentage?

The probability is 99.7​% that the sample percentage will be contained above _____ ​% and below _____ ​%.