​​​​1. f(x) = 1/2x-3 or y = 1/2x -3

1. The input is x and the output is f(x) or y. What is the slope of the function?
2. What is the y-intercept of the function?
3. What is the x-intercept of the function?
4. Graph the function.

1. What is the slope of a horizontal line?
2. Determine whether each function is increasing or decreasing?

f(x) = 4x + 3

a(x) = 5 -2x

k(x) = -4x +1

p(x) = 1/4x-3

q(x) = 4

4.

1. Find a linear equation satisfying the following condition

Passes through (2, 4) and (4, 10)

What is the solution to the following system of linear equations

2x+y = 15

3z -y = 5

Solve the system of equations by graphing

1. Find the midpoint of the line segment with the endpoints (7, -2) and (9, 5)
2. Find the midpoint of the line segment with endpoints (-2, -1) and (-8, 6).
3. If we invest $3,000 in an investment account paying 3% interest compounded quarterly, how much will the account be worth in 10 years?

1. From period 1 to period 2, weekly income increased from $100 to $106.5. What is the percentage change in income?
2. From period 1 to period 2, hourly wage increased from $12 to $15. What is the percentage change in hourly wage?

A certain region would like to estimate the proportion of voters who intend to participate in upcoming elections. A pilot sample of 25 voters found that 15 of them intended to vote in the election. Determine the additional number of voters that need to be sampled to construct a 98​% interval with a margin of error equal to 0.06 to estimate the proportion.

The region should sample _______________ additional voters. ​(Round up to the nearest​ integer.)

________________________________________________________________________________________________

A tire manufacturer would like to estimate the average tire life of its new​ all-season light truck tire in terms of how many miles it lasts. Determine the sample size needed to construct a 96​% confidence interval with a margin of error equal to 3,200 miles. Assume the standard deviation for the tire life of this particular brand is 7,000 miles.

The sample size needed is____ . ​(Round up to the nearest​ integer.)

Altobene, Inc.’s  R&D department recently conducted a test of three different brake systems to determine if there is a difference in the average stopping distance among the different systems.  In the test, 21 identical mid-sized cars were obtained from one of the major domestic carmakers.  Seven (7) cars were fitted with Brake A, seven (7) with Brake B, and seven (7) with Brake C. The number of feet required to bring the test cars to a full stop was recorded.

Which of the following is the appropriate null and alternative hypotheses about the stopping distance among the different systems?

H0: = =

HA: All of the population mean stopping distances are different from each other

H0:= =

HA: At least one population mean stopping distances is different from the others

H0:= =

HA: At least one population mean stopping distance is equal to another population mean stopping distance

Ho:= =  

Ha: Exactly one population mean stopping distance is greater than the other two population mean stopping distances

An ANOVA for the Stopping Distance Effect in Question 1 has been conducted with the partial results shown in the table below. Complete the ANOVA table.  

Source

Sum of Squares

Degrees of Freedom

Mean Square

F-Calculated

Between Groups (Brakes)

1314

Within Groups

XXXXXXXXXXXXX

Total

5299

20

What is the critical value of the test statistic for the brake stopping distance ANOVA if the hypothesis of interest is tested at the α = 0.01 level of significance?

6.013                                                  b.              5.092

4.938                                                  d.              3.127

Based on the ANOVA analysis, what conclusion would you make regarding the effect the braking system has on average stopping distance?

Reject HO, there is significant evidence to conclude there is a brake effect.

Do not reject HO, there is significant evidence to conclude there is a brake  effect.

Reject HO, there is insignificant evidence to conclude there is a brake effect.

Do not reject HO, there is insignificant evidence to conclude there is a brake effect.

1. (Chapter 14) The following data were obtained from a repeated-measures study comparing three treatment conditions.
   a. Use a repeated measures ANOVA with α=.05 to determine whether there are significant mean differences among the three treatments. (Hint: start by filling in the missing values on the table below). Be sure to show all formulas with symbols (and plug in numbers), steps, processes and calculations for all steps and all parts of all answers.
   b. Compute n², the percentage of variance accounted for by the mean differences, to measure the size of the treatment effects.  Be sure to show all formulas with symbols (and plug in numbers), steps, processes and calculations for all parts of all answers.

   Treatment	I	II	III	P-totals
   Person
   A	7	7	8	P=
   B	5	3	3	P=
   C	1	1	3	P=
   D	3	1	2	P=
   	M=	M=	M=		N=
   	T=	T=	T=		G=
   	SS=	SS=	SS=		Ex2=

Suppose that the number of printing mistakes on each page of a 200-page Mathematics book is independent of that on other pages. and it follows a Poisson distribution with mean 0.2.

(a) Find the probability that there is no printing mistake on page 23.

(b) Let page N be the first page which contains printing mistakes.

Find (i) the probability that N is less than or equal to 3,

(ii) the mean and variance of N.

(c) Let M be the number of pages which contain printing mistakes.Find the mean and variance of M.

(d) Suppose there is another 200-page Statistics book and there are 40 printing mistakes randomly and independently scattered through it.

Let Y be the number of printing mistakes on page 23.

(i) Which of the distributions - Bernoulli, binomial, geometric, Poisson, does Y follow?

(ii) Find the probability that there is no printing mistake on page 23.

Suppose the length of time an iPad battery lasts can be modeled by a normal distribu-tion with meanμ= 8.2 hours and standard deviationσ= 1.2 hours.

a. What is the probability that randomly selected iPad lasts longer than 10 hours?

b. What is the probability that a randomly selected iPad lasts between 7 and 10hours?

c. What is the 3rd percentile of the battery times?

d. Suppose 16 iPads are randomly selected. What is the probability that the meanlongevity ̄Xis less than 7.9 hours?

#2. You've sampled acorns from m^2 quadrates in Maine (the data are below). Based on these data, answer the following questions.

no.acorns<-c(3,26,11,24,22,16,15,26,20,22,17,16,18,20,18,15,17,16,12,25,22,20,27,19,13,17,17,20,25,26,13,21,12,27,19,15,14,20,17,15,15,23,27,17,17,14,18,23,18,23)

#A What is an appropriate distribution to use to model this data?

#B What is/are the parameter estimate(s) for this distribution?

Announcements for 84 upcoming engineering conferences were randomly picked from a stack of IEEE Spectrum magazines. The mean length of the conferences was 3.94 days, with a standard deviation of 1.28 days. Assume the underlying population is normal.

PART A:

Construct a 95% confidence interval for the population mean length of engineering conferences.

What is the lower bound of the confidence interval? (Round to 2 decimal places)

PART B:

Construct a 95% confidence interval for the population mean length of engineering conferences.

What is the upper bound of the confidence interval? (Round to 2 decimal places)

2. One‐Sample Univariate Hypothesis Testing with Proportions

For this question, show the results “by hand”, but you can use R to check your work. Suppose that the 4‐year graduation rate at a large, public university is 70 percent (this is the population proportion of successes). In an effort to increase graduation rates, the university randomly selected 200 incoming freshman to participate in a peer‐advising program. After 4 years, 154 of these students graduated. What are the null and alternative hypotheses? Can you conclude that this program was a success at the 5‐percent level of significance? Can you conclude that the program is a success at the 1‐percent level of significance? Show your work and explain. Since “success” is an increase in graduation rates, this is a one‐tailed test.

If X ~ N(108, 22.2), calculate the following:

a. P(X = 100, 108, 109, or 11) = _____.

If Y ~ N(-33, 10), then what is the distribution of (Y - (-33))/10?

b. (Y - (-33)/10 ~ N( _____ , _____ )

c. If X1 ~ N(111, 1123), then P(-122 < X1 < 765) = ________.

d. The distribution of (X1 - 111)/1123 is N( ____ , ____ ).

e. P(X1 >= 0) = _______.

f. P(X1 = 0) = _________.

If a doughnut shop offers seven different varieties of doughnut, how many different dozens of doughnuts can one order? Explain your answer.

The amount of time each week that Dunder Mifflin employees spend in pointless meetings follows a normal distribution with a mean of 90 minutes and standard deviation of 10 minutes.

A. What is the probability that employees spend between 81.5 and 103.5 minutes in meetings in a week?

B. The probability that employees spend between 80 and ???? minutes in meetings in a week is equal to 0.8351.

A pair of dice are rolled​ 1,000 times with the following frequencies of​ outcomes:

Use these frequencies to calculate the approximate empirical probabilities and odds for the events a. The sum is less than 3 or greater than 9.

b. The sum is even or exactly divisible by 5.

a. Probabilityequals = ___???

​(Type a​ decimal.)

Odds for = ____??

​(Type a fraction. Simplify your​ answer.)

b. Probabilityequals = ___???

​(Type a​ decimal.)

Odds for = ____??

​(Type a fraction. Simplify your​ answer.)

Select any data set . Use the method of Sections 6-6 to construct a histogram and normal quartile plot, then determine whether the data set appears to come from a normally distributed population.

When one company (A) buys another company(B), some workers of company B are terminated. Terminated workers get severance pay. To be fair, company A fixes the severance payment to company B workers as equivalent to company A workers who were terminated in the last one year. A 36-year-old Mohammed, worked for company B for the last 10 years earning 32000 per year, was terminated with a severance pay of 5 weeks of salary. Bill smith complained that this is unfair that someone with the same credentials worked in company A received more. You are called in to settle the dispute. You are told that severance is determined by three factors; age, length of service with the company and the pay. You have randomly taken a sample of 40 employees of company A terminated last year. You recorded

Number of weeks of severance pay

Age of employee

Number of years with the company

Annual pay in 1000s

Identify best subsets of variables based on Mallows Cp. What is the value of R-square to this “best” model? How many outliers are in the dataset? Use the criteria of your choice and mention it(them)