Explain the relationship between types or levels of data and types of statistical analyses available to such levels of data. Feel free to illustrate with examples

1.A. Dr. Smith purchased a network attached storage server with eleven 2TB hard drives in it. When he purchased the system, unknowingly to him, the supplier used hard drives from a bad manufacturing batch and thus among his drives there are four underperforming drives. (Underperforming drives have a much shorter lifetime.) They figured this out and since there is no way of determining which hard drives are faulty ahead of time (i.e., ahead of their death), they issued Dr. Smith a full refund and told him to keep the drives. He wanted to trash the drives but one of his students requested a few of them for his project. The student figured to use the drives in a RAID-1 configuration. (From Wikipedia : “A RAID 1 creates an exact copy (or mirror) of a set of data on two or more disks. This is useful when read performance or reliability is more important than data storage capacity.”) What are the chances that he is not going to lose any data prematurely if Dr. Smith gave him two, three, and four of the drives (what’s the probability for each of those setups)?

1.B. Same situation as in 1.A. However, the student is more adventurous, he wants to use RAID-5. (RAID 5 is a redundant array of independent disks configuration that uses disk striping with parity. Because data and parity are striped evenly across all of the disks, no single disk is a bottleneck. Striping also allows users to reconstruct data in case of a disk failure. RAID 5 evenly balances reads and writes, and is currently one of the most commonly used RAID methods. It has more usable storage than RAID 1 and RAID 10 configurations, and provides performance equivalent to RAID 0. RAID 5 groups have a minimum of three hard disk drives (HDDs) and no maximum. Because the parity data is spread across all drives, RAID 5 is considered one of the most secure RAID configurations.) How big of a virtual drive will he obtain and what are the chances that he is not going to lose any data prematurely if Dr. Smith gives him three or four of drives?
1.C. We are doing real time processing of data from 40 data sources. At the beginning of each time slot, each data source may (or may not) generate a data-set to be processed; the probability that any individual source actually generates a data-set is: 0.002 (and data sources are independent). In each time slot we can process up to two data-sets. As the processing is real time the processed results are only interesting if they are done within the time slot. What is the probability that we can process all incoming data-sets in any particular time slot?

Please show step by step work in a spreadsheet or excel so I can follow along:

A federal agency responsible for enforcing laws governing weights and measures routinely inspects packages to determine whether the weight of the contents is at least as great as that advertised on the package. A random sample of 30 containers whose packaging states that the contents weigh 8 ounces was drawn. The weight of each package in ounces can be found in the sheet entitled “Part 2 Question 4”. After conducting the appropriate test, can you conclude with confidence that packages that are labeled as weighing 8 ounces are likely to weigh 8 ounces?

Use three independent variables to test whether a region can support a high-tech manufacturing firm. Use descriptive and inferential statistics.

Consider a region of single stranded DNA 7 nucleotides long with the 5' end on the left. Assume any site in this region may be occupied with equal probability by any of the 4 bases A,T,G or C.

How many possible base sequences are possible?

What is the probability the sequence contains only the base G?

What is the probability the sequence contains only two type of bases?

What is the probability the sequence is CGTGAGA?

What is the probability the sequence does not contain any A or G bases?

What is the probability the sequence contains alternating G and C sequence?

1.Choose all that apply(2). For a cluster sample

All subjects have an equally likely chance of being selected

Clusters are usually determined by convenience

All subjects will be measured in a selected cluster

Clusters have to be of equal size

An equal number of subjects will be measured in every cluster

unanswered

2.A sampling bias occurs when

The sample is not selected at random

Subjects were influenced to respond a certain way

Subject did not respond

Subjects were given leading questions

3.Choose all that apply(2) for Population parameters.

Are rarely known

Are estimated from sample statistics

Are calculated from samples

Can be found by sampling a large portion of the population

unanswered

4.

You are trying to determine what the best combination of diet and exercise provides the most weight loss. You decided to try three different diets (Atkins, Paleo, McDonalds only), along with no dieting, and two different forms of exercise (Yoga, high cardio), along with no exercise. You try each combination possible, and track weight loss for each. What type of Experimental Design is this?

Completely Randomized Design

Latin Square Design

Completely Randomized Block Design

Factorial Design

unanswered

Determine the sample size n needed to construct a 90​% confidence interval to estimate the population proportion when p overbar=0.66 and the margin of error equals 8​%.

n=_______​(Round up to the nearest​ integer.)

___________________________________________________________________________

A restaurant would like to estimate the proportion of tips that exceed​ 18% of its dinner bills. Without any knowledge of the population​ proportion, determine the sample size needed to construct a 98​% confidence interval with a margin of error of no more than 6​% to estimate the proportion.

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

Compare the height, weight (in inches), and age for Eagles versus Patriots, using t tests. Provide the conclusions based on the t tests.

Eagles

Pats

1. In a random sample of 23 people, the mean commute time to work was 32.2 minutes and the standard deviation was 7.2 minutes. Assume the population is normally distributed and use a t-distribution to construct a 98% confidence interval for the population mean mu. What is the margin of error of mu? Interpret the results. Round to one decimal place as needed.

​​​​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?