A researcher studied the effects of three experimental diets with varying fat contents on

the total lipid (fat) level in plasma. Total lipid level is a widely used predictor of coronary heart disease.

Fifteen male subjects who were within 20 percent of their ideal body weight were grouped into five

blocks according to age. Within each block, the three experimental diets were randomly assigned to the

three subjects. Data on reduction in lipid level (in grams per liter) after the subjects were on the diet for

a fixed period of time follow.

Fat Content of Diet

Block		j=1	j=2	j=3
i		Extremely Low	Fairly Low	Moderately Low
1	Ages 15-24	.73	.67	.15
2	Ages 25-34	.86	.75	.21
3	Ages 35-44	.94	.81	.26
4	Ages 45-54	1.40	1.32	.75
5	Ages 55-64	1.62	1.41	.78

How would I obtain an analysis of variance table and test whether or not the mean reductions in lipid levels differ for the three diets using alpha(a = .05)?

   1.   Suppose that cans of creamed corn are produced in a normal distribution so that the average net content weight is 16.00 ounces per can, with a deviation of 0.12 ounces. What is the probability that a sample of 36 cans would have an average net content weight less than 15.91 ounces? Would this be an unusual or not unusal average weight for the sample?

.

2.   Suppose that cans of creamed corn are produced in a normal distribution so that the average net content weight is 16.00 ounces per can, with a deviation of 0.12 ounces. What is the third quintile for sample averages from  samples of 36 cans? (nearest thousandth)

  

3.   Suppose a 98% confidence interval is needed for the average weight of these cans of creamed corn is needed, because someone thinks the average is not the 16 ounces it was supposed to be. If this interval is to have a margin of error of  0.02 oz, how many data points will be needed for the new sample?

4.   Suppose that cans of creamed corn were supposed to be  produced so that the average net content weight is 16.00 ounces per can. However, a sample of 64 weights yields an average of 15. 953 ounces and a deviation of 0.0762 ounces. Use this sample information to create a 98% confidence interval for the population mean (round to the nearest thousandth of an ounce)

Can a six-month exercise program increase the total body bone mineral content (TBBMC) of young women?
That is, we are interested in determining if the exercise program is beneficial, i.e., the mean percent change is positive.

Assume a sample of 25 subjects is taken.

A team of researchers is planning a study to examine this question.
Based on the results, they are willing to assume that σ = 2 for the percent change in TBBMC over the six- month period.
They also believe that a change in TBBMC of 1% is important, so they would like to have a reasonable chance of detecting a change this large or larger.

Calculate the power of this test.

Use the step by step procedures: Social scientists have long been interested in the relationship between economic development and health. To gain some insight into this relationship, we can utilize data on the life expectancy of females from birth and GDP per capita. you’ll find data from 91 countries. Use the data in the sheet entitled “Part 2 Question 9” to calculate and interpret the correlation coefficient.

GNP	LExpF
600	75.5
2250	74.7
2980	77.7
2780	73.8
1690	75.7
1640	72.4
2242	74.0
1880	75.9
1320	74.8
2370	72.7
630	55.4
2680	67.6
1940	75.1
1260	69.2
980	67.6
330	66.1
1110	68.5
1160	66.5
2560	74.9
2560	72.8
2490	66.0
15540	76.8
26040	78.7
22080	77.7
19490	80.5
22320	78.4
5990	74.0
9550	76.7
16830	78.6
17320	79.9
23120	75.7
7600	72.4
11020	78.6
23660	80.0
34064	80.0
16100	77.9
17000	79.6
25430	81.8
20470	79.8
21790	78.3
168	42.0
6340	69.4
2490	55.0
3020	64.8
10920	77.4
1240	67.8
16150	75.4
5220	65.8
7050	65.2
1630	65.8
19860	72.9
210	56.0
380	70.9
14210	80.1
350	52.1
570	62.0
2320	71.6
110	62.5
170	48.1
380	59.2
730	66.1
11160	74.0
470	71.7
1420	68.9
2060	63.3
610	46.1
2040	59.7
1010	55.3
600	60.3
120	45.6
390	53.2
260	44.6
390	55.8
370	60.5
5310	62.6
200	41.2
960	62.5
80	48.1
1030	57.5
360	52.2
240	42.6
120	46.6
2530	63.5
480	51.0
810	49.5
1440	66.4
220	52.7
110	54.7
220	53.7
420	52.5
640	60.1

(1) Using a similar dataset in “Part 2 Question 10”, calculate and interpret the correlation coefficient for the data on a life expectancy of males from birth and GDP per capita.

GNP	LExpM
600	69.6
2250	68.3
2980	71.8
2780	65.4
1690	67.2
1640	66.5
2242	64.6
1880	66.4
1320	66.4
2370	65.5
630	51.0
2680	62.3
1940	68.1
1260	63.4
980	63.4
330	60.4
1110	64.4
1160	56.8
2560	68.4
2560	66.7
2490	62.1
15540	70.0
26040	70.7
22080	71.8
19490	72.3
22320	71.8
5990	65.4
9550	71.0
16830	72.0
17320	73.3
23120	67.2
7600	66.5
11020	72.5
23660	74.2
34064	73.9
16100	72.2
17000	73.3
25430	75.9
20470	73.0
21790	71.5
168	41.0
6340	66.8
2490	55.8
3020	63.0
10920	73.9
1240	64.2
16150	71.2
5220	62.2
7050	61.7
1630	62.5
19860	68.6
210	56.9
380	68.0
14210	74.3
350	52.5
570	58.5
2320	67.5
110	60.0
170	50.9
380	59.0
730	62.5
11160	68.7
470	67.8
1420	63.8
2060	61.6
610	42.9
2040	52.3
1010	50.1
600	57.8
120	42.4
390	49.9
260	41.4
390	52.2
370	56.5
5310	59.1
200	38.1
960	59.1
80	44.9
1030	55.0
360	48.8
240	39.4
120	43.4
2530	57.5
480	48.6
810	42.9
1440	64.9
220	49.9
110	51.3
220	50.3
420	50.4
640	56.5

1) Design a study that uses a dependent samples design

2) Design a study that uses an independent samples design. Be sure to make clear your independent and dependent variables.

Base your two studies on the same general idea.

B. In a test of the effect of dampness on electric connections, 100 electric connections were tested under damp conditions and 150 were tested under dry conditions. Twenty of the damp connections failed and only 10 of the dry ones failed.

(i) Conduct a hypothesis test with α = 0.10 to determine whether or not there is a greater proportion of connections which fail under damp conditions compared to dry conditions. Be sure to state your hypotheses, test statistic, p-value, and conclusions.

(ii) Construct a 90% two-sided confidence interval for the difference of proportions πdamp −πdry. Compare the CI with the results of the hypothesis test in (i). Are the conclusions consistent?

This question is modified from an actual experiment published in a medical journal. A study claimed that people who eat high-fibre cereal for breakfast will on average consume fewer calories for lunch than people who do not eat high-fibre cereal for breakfast. A group of 150 people were randomly selected. Each person was identified as either a consumer or a non-consumer of high-fibre cereal at breakfast, and the number of calories consumed at lunch was measured and recorded. Here are the data. (Numbers are fictitious.)
(a) Calories consumed at lunch by high-fibre breakfast consumers:

568 646 607 555 530 714 593 647 650 498 636 529 565 566 639 551 580 629
589 739 637 568 687 693 683 532 651 681 539 617 584 694 556 667 467 540

596 633 607 566 473 649 622

(b) Calories consumed at lunch by low-fibre breakfast consumers:
705 754 740 569 593 637 563 421 514 536
819 741 688 547 723 553 733 812 580 833
706 628 539 710 730 620 664 547 624 644
509 537 725 679 701 679 625 643 566 594
613 748 711 674 672 599 655 693 709 596
582 663 607 505 685 566 466 624 518 750
601 526 816 527 800 484 462 549 554 582
608 541 426 679 663739 603 726 623 788
787 462 773 830 369 717 646 645 747
573 719 480 602 596 642 588 794 583
428 754 632 765 758 663 476 490 573
Test if the result of the study is statistically significant at 5% significance level. (COULD YOU PLEASE DESCRIBE ALL THE STEPS ONE BY ONE IN YOUR CALCULATION?) Thank you in advance for your help.

​

The U.S. Bureau of Mines produces data on the price of Minerals. The data below displays the average prices per year for several minerals over a decade.

Gold ($ per oz.)	Copper (cents per lb.)	Silver ($ per oz.)	Aluminum (cents per lb.)
161.1	64.2	4.4	39.8
308.0	93.3	11.1	61.0
613.0	101.3	20.6	71.6
460.0	84.2	10.5	76.0
376.0	72.8	8.0	76.0
424.0	76.5	11.4	77.8
361.0	66.8	8.1	81.0
318.0	67.0	6.1	81.0
368.0	66.1	5.5	81.0
448.0	82.5	7.0	72.3
438.0	120.5	6.5	110.1
382.6	130.9	5.5	87.8

Use the attached MS Excel spreadsheet data and multiple regression to produce a model to predict the average price of gold from other variables. Comment on the following:

1. Regression equation
2. R, R2 and 1-R2, adjusted R2
3. Standard error of estimate
4. Report the t's for each value and the corresponding p-values
5. Overall test of hypothesis and decision
6. Use a .05 level of significance. Cite which variables are significant and which are not significant, based on the t values and p values for each independent variable.

A store sold 12 stereos on Monday, 17 on Tuesday, 28 on Wednesday, 17 on Thursday and 26 on Friday. AT the .01 level, test if there is a difference in the number of stereos sold on each weekday. State the hypotheses and identify the claim, find the critical value(s), compute the test value, make the decision and summarize the results. Show all work and formulas - sample question that I don't get.

A local university wants to conduct a sample of 200 students out of 6000 students. We can assume that the university maintains a good roster of all registered students. (1) how would you select the 200 students(a) using simple random sample method and (b) systematic sampling method? (2) suppose that the university administration wants to make sure in particular students who major in music (a small department with only 8% of students major in music)be adequately included in your sample, how would you go about selecting a sample ?

The conference Board produces a Consumer Confidence Index (CCI) that reflects people's feelings about general business conditions, employment opportunities, and their own income prospects. Some researchers may feel that consumer confidence is a function of the median household income.

Use the attached MS Excel spreadsheet containing the CCIs for nine years and the median household incomes for the same nine years published by the U.S. Census Bureau.

Perform a correlation and regression analysis to predict CCI using median household income. Discuss the following:

1. Scatter Diagram
2. R, R2 and 1-R2
3. The regression equation
4. Standard error of estimate
5. The test of hypothesis with the 5-step process. Use a .05 level of significance. Does median household income appear to be good predictor of the CCI? Why or why not?

CCI	Median House Hold Income ($1,000)
116.8	37415
91.5	36770
68.5	35501
61.6	35047
65.9	34700
90.6	34942
100	35887
104.6	36306
125.4	37005

A widget produced by a particular process has probability .1 of being defective. A test can be performed which has 99% accuracy. That is, if a defective widget is tested, the test will identify the widget as defective 99% of the time. And if a non-defective widget is tested, there is a 99% chance that the test will indicate that the widget is not defective. One widget is selected at random and is tested. If the test says that the widget is not defective, what is the probability that the widget actually is defective?

QUESTION 1

The fundalmental condition that permits proper statistical inference is

	a.	having a large sample
	b.	normal distribution of scores
	c.	random sampling
	d.	knowledge of the values of the parameters of the population

QUESTION 2

Randomization and random sampling

	a.	can be substituted for each other
	b.	often amount to the same thing
	c.	are different procedures
	d.	are synonymous

QUESTION 3

Randomization is used to

	a.	assigning participants to experimental conditions
	b.	to analyze data from random samples.
	c.	as a less complex substitute for random sampling
	d.	to select subjects randomly from a population

QUESTION 4

A population characteristic is known as a(n)

	a.	parameter
	b.	basic value
	c.	element
	d.	statistic

QUESTION 5

"statistic" is to "parameter" as

	a.	"calculated" is to "given"
	b.	"random sampling" is to "randomization"
	c.	"sample" is to "populaton"
	d.	"mean" is to "standard deviation"

QUESTION 6

Whether or not a sample is considered random depends on

	a.	the method of selection
	b.	how closely it resembles the population
	c.	the size of the sample
	d.	None of the above

QUESTION 7

Each score in a random sampling distribution of means represents

	a.	a random data point
	b.	a single individual
	c.	a standard score
	d.	a sample mean

QUESTION 8

Which of the following is a parameter?

	a.	σ
	b.	Xbar
	c.	r
	d.	s

QUESTION 9

The standard error of the mean

	a.	is a standard deviation
	b.	is the average amount by which sample values are in error
	c.	is given in terms of standard units
	d.	is larger for larger populations

QUESTION 10

A sampling distribution is a distribution of

	a.	values of a statistic obtained from samples
	b.	scores obtained from samples
	c.	values of a parameter obtained from samples
	d.	any of the above

The equation of a regression line, unlike the correlation, depends on the units we use to measure the explanatory and response variables. Here is the data on percent body fat and preferred amount of salt. Preferred amount of salt x 0.2 0.3 0.4 0.5 0.6 0.8 1.1 Percent body fat y 19 31 22 29 39 24 31 In calculating the preferred amount of salt, the weight of the salt was in milligrams. (a) Find the equation of the regression line for predicting percent body fat from preferred amount of salt when weight is in milligrams. (Round your answers to one decimal place.) ŷ = + x (b) A mad scientist decides to measure weight in tenths of milligrams. The same data in these units are as follows. Preferred amount of salt x 2 3 4 5 6 8 11 Percent body fat y 19 31 22 29 39 24 31 Find the equation of the regression line for predicting percent body fat from preferred amount of salt when weight is in tenths of milligrams. (Round your intercept to one decimal place and your slope to two decimal places.) ŷ = + x (c) Use both lines to predict the percent body fat from preferred amount of salt for a child with preferred amount of salt 0.9 when weight is measured in milligrams, which is the same as 9 when weight is in tenths of milligrams. (Round your answers to one decimal place.) in milligrams % body fat in tenths of milligrams % body fat Are the two predictions the same (up to any roundoff error)? Yes No

A stationary store has decided to accept a large shipment of ballpoint pens if an inspection of 20 randomly selected pends yields no more than two defective pens. (a) Find the probability that this shipment is accepted if 5% of the total shipment is defective. (b) Find the probability that this shipment is not accepted if 15% of the total shipment is defective. Kindly use the numbers given in the word sentences to show the work. Thank you