An experiment was performed on a certain metal to determine if the strength is a function of heating time (hours). Results based on 25 metal sheets are given below. Use the simple linear regression model.

∑X = 50

∑X2 = 200

∑Y = 75

∑Y2 = 1600

∑XY = 400

Find the estimated y intercept and slope. Write the equation of the least squares regression line and explain the coefficients. Estimate Y when X is equal to 4 hours. Also determine the standard error, the Mean Square Error, the coefficient of determination and the coefficient of correlation. Check the relation between correlation coefficient and Coefficient of Determination. Test the significance of the slope.

Please show all work, please type out so it is legible, thank you

In a randomized comparative experiment on the effect of color on the performance of a cognitive task, researchers randomly divided 68 subjects (26 males and 42 females ranging in age from 17 to 25 years) into three groups. Participants were asked to solve a series of 6 anagrams. One group was presented with the anagrams on a blue screen; one group saw them on a red screen; and one group had a neutral screen. The time, in seconds, taken to solve the anagrams was recorded. The paper reporting the study gives x¯= 11.51 and s= 4.25 for the times of the n= 21 members of the neutral group. (Give your answer to three decimal places.) A 95 % confidence interval for the mean time in the population from which the subjects were recruited is from to seconds.

It was believed from the experiment on the obstacle course, in Part I, that there is a relationship between a subject’s reaction time before drinking two beers and the subject’s age:

Experiment carried out in part I

Drunk driving is one of the main causes of car accidents. Interviews with drunk drivers who were involved in accidents and survived revealed that one of the main problems is that drivers do not realise that they are impaired, thinking “I only had 1-2 drinks … I am OK to drive.” A sample of 5 drivers was chosen, and their reaction times (seconds) in an obstacle course were measured before and after drinking two beers. The purpose of this study was to check whether drivers are impaired after drinking two beers. Below is the data gathered from this study

Driver 1 2 3 4 5

Before 6.15 2.86 4.55 3.94 4.19

After 6.85 4.78 5.57 4.01 5.72

Driver 1 2 3 4 5

Age (years) 20 30 25 27 26 1.

(a)What type of study is being outlined here? Justify your answer?

(b)Plot a graph representing the relationship between reaction times before drinking two beers and age.

(c) From the graph in (b), suggest a relationship that could exist between the two measurements?

(d)Use a 1% level of significance and the following points to test the claim that there is a relationship between the reaction times before drinking two beers and age.

(i) State the null and alternative hypotheses in context

.(ii) Calculate the test statistic.

(e) Identify the rejection region(s).

(f) Clearly state your conclusions (in context).

(g)What percentage of variation in reaction times before drinking two beers is unexplained by the relationship between reaction times before drinking two beers and age?

(h) Derive a model/equation that could be used to predict reaction times before drinking two beers for a person, if the age of the person is known.

(i) Using the model derived in (h), what would the predicted reaction time, in the obstacle course, before drinking two beers of a 22-year-old be?

(20.30) In a randomized comparative experiment on the effect of color on the performance of a cognitive task, researchers randomly divided 70 subjects (24 males and 46 females ranging in age from 17 to 25 years) into three groups. Participants were asked to solve a series of 6 anagrams. One group was presented with the anagrams on a blue screen; one group saw them on a red screen; and one group had a neutral screen. The time, in seconds, taken to solve the anagrams was recorded. The paper reporting the study gives x¯¯¯=x¯=11.73 and s=s=4.19 for the times of the 24 members of the neutral group.

(Give your answer to three decimal places.)

A 96 % confidence interval for the mean time, when using a neutral screen, in the population from which the subjects were recruited is from  to  seconds.

3. An experiment was conducted to evaluate the effectiveness of a treatment for tapeworm in the stomachs of sheep. A random sample of 24 worm-infected lambs of approximately the same age and health was randomly divided into two groups. Twelve of the lambs were injected with the drug and the remaining twelve were left untreated. After 6 months, the lambs were slaughtered and the following worm counts were recorded. Assume the counts are approximately normally distributed.

Drug-treatedsheep 18, 43, 28, 50, 16, 32, 13, 35, 38, 33, 6, 7

Untreatedsheep 40, 54, 26, 63, 21, 37, 39, 23, 48, 58, 23, 39

1. Construct a 98% confidence interval for the difference of the worm count in a lamb.
2. Please perform a statistical test and see if the drug treatment reduced the mean worm count in a lamb. Use the significance level 0.05.
3. What are your assumptions that you assumed in part (b)?

Monica and Dylan are doing a “thought experiment”. They are imagining that Monica is in a space ship orbiting a black hole, just outside the event horizon, while Dylan is in a space ship 1 light year away. Monica and Dylan each send each other a signal using a laser. From each of their perspectives, their laser flashes once a second. To Dylan, is Monica’s laser flashing faster, slower or at the same rate (once a second)? Similarly, how fast does Dylan’s laser appear to be flashing from Monica’s point of view?

9. An experiment was performed on a certain metal to determine if the strength is a function of heating time (hours). Results based on 20 metal sheets are given below. Use the simple linear regression model.

∑X = 40

∑X2 = 200

∑Y = 80

∑Y2 = 1120

∑XY = 388

Find the estimated y intercept and slope. Write the equation of the least squares regression line and explain the coefficients. Estimate Y when X is equal to 5 hours. Also determine the standard error, the Mean Square Error, the coefficient of determination and the coefficient of correlation. Check the relation between correlation coefficient and Coefficient of Determination. Test the significance of the slope.

An experiment was conducted to evaluate the effectiveness of a treatment for tapeworm in the stomachs of sheep. A random sample of 24 worm-infected lambs of approximately the same age and health was randomly divided into two groups. Twelve of the lambs were injected with the drug and the remaining twelve were left untreated. After 6 months, the lambs were slaughtered and the following worm counts were recorded. Assume the counts are approximately normally distributed.

Drug-treatedsheep 18 43 28 50 16 32 13 35 38 33 6 7

Untreatedsheep   40 54 26 63 21 37 39 23 48 58 23 39

(a) Construct a 98% confidence interval for the difference of the worm count in a lamb.

(b) Please perform a statistical test and see if the drug treatment reduced the mean worm count in a lamb. Use the significance level 0.05.

(c) What are your assumptions that you assumed in part (b)?

In a randomized comparative experiment on the effect of color on the performance of a cognitive task, researchers randomly divided 69 subjects (28 males and 41 females ranging in age from 17 to 25 years) into three groups. Participants were asked to solve a series of 6 anagrams. One group was presented with the anagrams on a blue screen; one group saw them on a red screen; and one group had a neutral screen. The time, in seconds, taken to solve the anagrams was recorded. The paper reporting the study gives x⎯⎯⎯= x ¯ = 11.54 and s= s = 4.35 for the times of the 25 members of the neutral group. (Give your answer to three decimal places.) A 96 % confidence interval for the mean time, when using a neutral screen, in the population from which the subjects were recruited is from to seconds.

15. In an experiment, an independent variable is _______ and a dependent variable is _______.

Group of answer choices

Manipulated, measured

Measured, manipulated

Discrete, summation

Continuous, manipulated

16. Outliers are

Group of answer choices

The lowest and highest scores in a data set

Extreme or unusual values

All options present

The lowest value in a data set

17. Assume that we have the following set of data:

    Score                 11, 12, 17, 18, 19, 20, 21, 22, 23, 24, 25
    Frequency         2, 1, 5,    8, 6, 12, 13, 10, 15, 9, 8.

These data would most likely characterized as

Group of answer choices

Negatively skewed

Normal

Uniformly distributed

Positively skewed

18. For the data referred to in the previous question, the distribution would best be called

Group of answer choices

Symmetric

Bimodal

Unimodal

Balanced

19. The onset of eating disorders was shown to occur most often during puberty and during the late teen years in girls.  A distribution of the frequencies of onset of eating disorders by age would most likely be

Group of answer choices

All options present

Unimodal

Normal

Bimodal

20. Which of the following distributions can be symmetric?

Group of answer choices

All options present

Bimodal

Normal

Unimodal

21. If the distribution of the ages of people were positively skewed, which of the following is most likely correct?

Group of answer choices

There are more young people than old people

There are about the same number of young people as old people

There are more old people than young people

None of the options present

22. A negatively skewed distribution

Group of answer choices

Is symmetric

Has a long tail pointing to the left

Has a long tail pointing to the right

Is also positively skewed

23. The best measure of central tendency

Group of answer choices

Is the mode

Depends on the data and the question you want to ask.

Is the median

Is the mean

24. For the following set of data [5   9   5   5   2   4], the mean is

Group of answer choices

4

4.5

6

5

25. The median has at least one advantage over the mean in that

Group of answer choices

It is easier to calculate than the mode

It is not much affected by extreme scores

It varies less from sample to sample

It is usually closer to the population mean than the mode

26. The median location is

Group of answer choices

The position, in an ordered series, occupied by the median

The number of scores that occur at the median

The highest point on a frequency distribution

The number closest to the mean

27. The mode of the numbers 1   3   4   5   6   6   7   8   9   9   9 is

Group of answer choices

6.1

9

6.5

6

28. We are most likely to randomly pick which score from an actual data set?

Group of answer choices

The lowest score

The median

The highest score

The mode

29. The chief advantage of the median is that

Group of answer choices

It is not disproportionately affected by extreme scores

It is the most commonly occurring score

It is best used with nominal scales

It represents a score actually occurring in the data set

30. The chief disadvantage of the median, when compared to the mean, is that

Group of answer choices

It is disproportionately affected by outliers

It is less stable than the mean from sample to sample

Its location cannot be calculated algebraically

It has no disadvantages

31.The most commonly used measure of central tendency is

Group of answer choices

The mode

The mean

All are equally common

The median

32. When the distribution is symmetric, which of the following are always equal?

Group of answer choices

Median and mode

Mean, median, and mode

Mean and mode

Mean and medi

33. When  the distribution is symmetric and unimodal, which of the following are always equal?

Group of answer choices

Mean and median

Mean, median, and mode

Median and mode

Mean and mode

34.  is the symbol commonly used for the

Group of answer choices

Mean

Median

Mode

None of the options present

35. Dispersion refers to

Group of answer choices

All options present

The degree to which individual data points are distributed around the mean

The centrality of the distribution

The degree to which data cluster toward one end of the scale

36. An outlier

Group of answer choices

Can be an error and/or an extreme score

Can be an error that snuck into the data

Can be an extreme score

Will never have a large influence on many measures of variability

37. The population variance is

Group of answer choices

An estimate of the sample variance

Usually an unknown that we try to estimate

Calculated exactly like the sample variance

A biased estimate

38. The difference between s and σ  is that σ is

Group of answer choices

The long range average of the variance over repeated sampling

The value of the standard deviation in a population

The biased estimate of s

The value of the standard deviation in a sample

39. Data points at the extremes of the distribution have

Group of answer choices

Little effect on the variance

More effect on the variance than scores at the center of the distribution

Distort the usefulness of the median

Are undoubtedly incorrect

40. Which of the following sets of data is likely to have the smallest standard deviation?

Group of answer choices

The grade point averages of students from your high school’s honors biology class

The distribution of heights of students in an elementary school

The amount that you and your friends pay for college tuition

The distribution of SAT scores for students from your high school

41. If we multiply a set of data by a constant, such as converting feet to inches, we will

Group of answer choices

Leave the mean and variance unaffected

Multiply the mean by the constant but leave the standard deviation unchanged

Multiply the mean and the standard deviation by the constant

Leave the mean unchanged but alter the standard deviation

42. The range is

Group of answer choices

Not influenced very much by outliers

The difference between the inner fences

The difference between the highest and lowest score

The H-spread

43. Three variables, A, B and C, follow:

A            10          15          20          25          30          35          40
B            25          23          15          12          10          8            5
C            10          13          16          25          47          50          75

Their means are

Group of answer choices

12.10, 15.38, 74.56

23.33, 26.50, 28.65

25.25, 21.25, 52.21

25.00, 14.00, 33.71

10.15, 32.65, 45.32

44. Their Standard Deviations are

Group of answer choices

13.11, 11.54, 9.41

54.63, 65.52, 67.58

33.21, 41.37, 45.82

10.80, 7.53, 24.25

15.31, 10.05, 5.48

45. SPSS will always conduct the correct analyses

Group of answer choices

False

True