Questions
The following data were obtained from a repeated-measures study comparing 3 treatment conditions. Use a repeated-measures...

The following data were obtained from a repeated-measures study comparing 3 treatment conditions. Use a repeated-measures ANOVA with a=.05 to determine whether there are significant mean differences among the three treatments (do all 4 steps of conducting a hypothesis test!!):

Person

Treatment 1

Treatment 2

Treatment 3

Person Totals

A

0

2

4

P=6

N=15

B

0

3

6

P=9

G=60

C

3

7

8

P=18

D

0

7

5

P=12

E

2

6

7

P=15

M=1

M=5

M=6

T=5

T=25

T=30

SS=8

SS=22

SS=10

In: Math

A measure of the strength of the linear relationship that exists between two variables is called:...

A measure of the strength of the linear relationship that exists between two variables is called: Slope/Intercept/Correlation coefficient/Regression equation. If both variables X and Y increase simultaneously, then the coefficient of correlation will be: Positive/Negative/Zero/One. If the points on the scatter diagram indicate that as one variable increases the other variable tends to decrease the value of r will be: Perfect positive/Perfect negative/Negative/Zero. The range of correlation coefficient is: -1 to +1/0 to 1/-∞ to +∞/0 to ∞. Which of the following values could NOT represent a correlation coefficient? r = 0.99/r = 1.09/r = -0.73/r = -1.0. The correlation coefficient is used to determine: A specific value of the y-variable given a specific value of the x-variable/A specific value of the x-variable given a specific value of the y-variable/The strength of the relationship between the x and y variables/None of these. If two variables, x and y, have a very strong linear relationship, then: There is evidence that x causes a change in y/There is evidence that y causes a change in x/There might not be any causal relationship between x and y/None of these alternatives is correct. If the Pearson correlation coefficient R is equal to 1 (r=1) then: There is a negative relationship between the two variables. /There is no relationship between the two variables. /There is a perfect positive relationship between the two variables. /There is a positive relationship between the two variables. If the correlation between 2 variables is -.77, which of the following is true? There is a fairly strong negative linear relationship/An increase in one variable will cause the other variable to decline by 75%

In: Math

a random sample of 175 xray machines is taken. and 54 machines in the sample malfunction....

a random sample of 175 xray machines is taken. and 54 machines in the sample malfunction. compute a 95% confidence interval for the proportion of all xray machines that malfunction. then calculate the upper and lower limit of the 95% confidence intervals

In: Math

In a recent marketing campaign, Olive Garden Italian Restaurant® offered a “NeverEnding Pasta Bowl.” The customer...

In a recent marketing campaign, Olive Garden Italian Restaurant® offered a “NeverEnding Pasta Bowl.” The customer could order an array of pasta dishes, selecting from 7 types of pasta and 6 types of sauce, including 2 with meat.

a. If the customer selects one pasta type and one sauce type, how many “pasta bowls” can the customer order?

b. How many different “pasta bowls” can the customer order without meat?

In: Math

Question 11 (CO 4) Seventy-nine percent of products come off the line ready to ship to...

Question 11

(CO 4) Seventy-nine percent of products come off the line ready to ship to distributors. Your quality control department selects 12 products randomly from the line each hour. Looking at the binomial distribution, if fewer than how many are within specifications would require that the production line be shut down (unusual) and repaired?

Fewer than 7
Fewer than 9
Fewer than 6
Fewer than 10

Question 12

(CO 4) Out of each 100 products, 96 are ready for purchase by customers. If you selected 21 products, what would be the expected (mean) number that would be ready for purchase by customers?

20
96
21
26

In: Math

1) The first task is to review some information that might be useful later: a) Write...

1) The first task is to review some information that might be useful later:

a) Write a brief definition of the word "quartile" as we have used it in previous weeks. Be sure to provide a citation: _____________________________.

b) Write a brief definition of the word "quantile" as it might be used in statistics. Be sure to provide a citation (do not cut and paste... use your own words to summarize what you discovered): ________________________________.

c) From within interactive R, enter the command shown below (the command shows a help page for the pbinom command). Provide a very brief description of the arguments that are passed to the pbinom() command ("arguments" in computer programming are the options that you give to a function so that the function can calculate what you want it to). Note that one of the arguments is lower.tail = TRUE, and because there is a value assigned to it with the equals sign, it means that if you do not enter a new value for lower.tail, it will be set to TRUE by default. Do not type the ">" into R, it is the command prompt:

> ?pbinom

2) You can use the dbinom() command (function) in R to determine the probability of getting 0 heads when you flip a fair coin four times (the probability of getting heads is 0.5):

dbinom(0, size=4, prob=0.5)

Find the equivalent values for getting 1, 2, 3, or 4 heads when you flip the coin four times. TIP: after you run the first dbinom() command, press the up arrow and make a small change and run it again.

probability of getting exactly 1 head: _______

probability of getting exactly 2 heads: _______

probability of getting exactly 3 heads: _______

probability of getting exactly 4 heads: _______

3) Use the pbinom() function in R to show the cumulative probability of getting 0, 1, 2, 3, or 4 heads when you flip the coin 4 times (this is the same as finding the probability than the value is less than or equal to 0, 1, 2, 3, or 4.)

probability of getting no more than 0 heads: ____

probability of getting no more than 1 head: _____

probability of getting no more than 2 heads:_____

probability of getting no more than 3 heads: ____

probability of getting no more than 4 heads: ____

4) The following R command will show the probability of exactly 6 successes in an experiment that has 10 trials in which the probability of success for each trial is 0.5:

dbinom(6, size=10, prob=0.5)
(True/False)____________

5) What is the probability of getting fewer than 2 heads when you flip a fair coin 3 times (round to 2 decimal places) ? ______

6) What is the probability of getting no more than 3 heads when you flip a fair coin 5 times (be sure to understand the wording differences between this question and the previous one—round to 2 decimal places)? ________

---------------------------------------------------

Information

The exponential distribution is a continuous distribution. The main R functions that we will use for the exponential distribution are pexp() and qexp(). Here is an example of the pexp() function. Leaves are falling from a tree at a rate of 10 leaves per minute. The rate is 10, or we can say that lambda = 10 (meaning 10 leaves fall per minute). The leaves do not fall like clockwork, so the time between leaves falling varies. If the time between leaves falling can be modeled with an exponential distribution, then the probability that the time between leaves falling will be less than 5 seconds (which is 5/60 of a minute) would be:

(note: this is an explanation of how pexp() works, you will answer a different question below)

pexp(5/60, rate=10)

which is about 0.565 (meaning that the probability is a bit higher than 50% that the next time-span between leaves falling will be less than 5 seconds).

For tasks 7-12, assume that the time interval between customers entering your store can be modeled using an exponential distribution. You know that you have an average of 4 customers per minute, so the rate is 4, or you can say that lambda =4.

It is easiest to keep everything in the original units of measurement (minutes), but you can also translate that to seconds because a rate of “4 customers per minute” is the same as “4 customer per 60 seconds,” and you can divide each number by 4 to get a rate of “1 customer per 15 seconds” or a rate of “1/15 customers per second.”

7) What is the expectation for the time interval between customers entering the store? Be sure to specify the units of measurement in your answer. Round to 3 decimal places: ___________________

8) What is the variance of the the time interval? Be sure to specify the units of measurement in your answer. Round to 3 decimal places:_________________

9) The pexp() function is introduced at the bottom of Yakir, 2011, p. 79, and there are some tips above. What is the probability that the time interval between customers entering the store will be less than 15.5 seconds. Be sure to enter values so that everything is in the same unit of measurement. Be sure to specify the units of measurement in your answer. Round your answer to 3 decimal places: _________________.

10) What is the probability that the time interval between customers entering the store will be between 10.7 seconds and 40.2 seconds?________

11) The qexp() function in R allows you to enter a probability, and it will tell you the criterion value (“cutoff point”) that corresponds to that probability value (e.g., if you enter .05 it tells you the cutoff point below which 5% of the values in the distribution fall).

What value of x would be the criterion value (cut-off point) for the top 5% of time intervals (Round to 3 decimal places, and include the units of measurement)? _______

---------------------------------

12) Describe in your own words the meaning of the number that the following R command produces (you are asked to interpret the resulting number so that we understand what that number means).

pexp(1.2, rate=3)

---------------------------------

Information

You have now had practice with the binomial distribution and the exponential distribution. The approach to solving problems for the normal distribution is similar to that for the exponential function, but obviously you use different R functions (usually pnorm() or qnorm()).

For the following three exercises, assume that you have a normally distributed random variable, called A, with a mean of 7, and a population standard deviation of 3.

13) What is the probability that a randomly selected value from variable A will be greater than 9?_______

14) What value of variable A would be the cutoff point (criterion value) for identifying the lowest 4% of values in variable A (use the qnorm function)?____________

15) What is the probability that a randomly selected value from variable A will be more than one standard deviation above its mean (there are couple ways to solve this, one way is to use the standard normal distribution?________________

In: Math

A study commissioned by the power company shows that of 9,848 persons residing within 500 yards...

A study commissioned by the power company shows that of 9,848 persons residing within 500 yards of high voltage lines, 600 have developed one of the cancers in question. Of 13,112 living more than 500 yards from such lines, 550 contracted one of the cancers. a. Calculate the point estimate of odds ratio b. Calculated 95% confidence interval of the odds ratio. Does the odds ratio significantly different from 1?

In: Math

A large tank of fish from a hatchery is being delivered to a lake. The hatchery...

A large tank of fish from a hatchery is being delivered to a lake. The hatchery claims that the mean length of fish in the tank is 15 inches, and the standard deviation is 4 inches. A random sample of 28 fish is taken from the tank. Let x be the mean sample length of these fish. What is the probability that x is within 0.5 inch of the claimed population mean? (Round your answer to four decimal places.)

In: Math

1. One method for obtaining random numbers is by Middle Square method, you are asked to...

1. One method for obtaining random numbers is by Middle Square method, you are asked to create an algorithm to get a random number with an 6 digit integer number. And give an example.

In: Math

-Identify why you choose to perform the statistical test (Sign test, Wilcoxon test, Kruskal-Wallis test). -Identify...

-Identify why you choose to perform the statistical test (Sign test, Wilcoxon test, Kruskal-Wallis test).

-Identify the null hypothesis, Ho, and the alternative hypothesis, Ha.

-Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.

-Find the critical value(s) and identify the rejection region(s).

-Find the appropriate standardized test statistic. If convenient, use technology.

-Decide whether to reject or fail to reject the null hypothesis.

-Interpret the decision in the context of the original claim.

A weight-lifting coach claims that weight-lifters can increase their strength by taking vitamin E. To test the theory, the coach randomly selects 9 athletes and gives them a strength test using a bench press. Thirty days later, after regular training supplemented by vitamin E, they are tested again. The results are listed below. Use the Wilcoxon signed-rank test to test the claim that the vitamin E supplement is effective in increasing athletes' strength. Use α = 0.05.

Athlete

1

2

3

4

5

6

7

8

9

Before

185

241

251

187

216

210

204

219

183

After

195

246

251

185

223

225

209

214

188

In: Math

Please answer all parts, it is not that lengthy. If you can't answer last parts, don't...

Please answer all parts, it is not that lengthy. If you can't answer last parts, don't attempt then . Leave for someone else

A manufacturing process produces defective items 15% of the time. A random sample of 80 items is taken from the 3000 produced on a particular day, and each sampled item is tested to see if it is defective or not.
In the context of this problem, identify each of the following:
a. Population:
b. Parameter of interest:
c. Sampling frame:
d. Sample:
e. Sampling method:
f. Is there any potential bias? Explain your answer.

In: Math

You are an analyst for the Coral Cola Company and are interested in the association between...

You are an analyst for the Coral Cola Company and are interested in the association between age and rating of a new type of soda (Irish-Cream Cream-Soda). You suspect that younger individuals will prefer the soda over older individuals which could be useful for developing advertisement programs that can appeal to the population that likes Irish-Cream Cream-Soda the most (e.g., younger individuals). You conduct a study in which you allow participants (n = 15) to taste the new soda and rate how much they like it on a scale from 1 – 10 (1 being the “worst thing I ever tasted” to 10 being the “best thing I ever tasted”). In addition, you record their age. Use the 6 steps of hypothesis testing and SPSS to determine whether there is an association between ratings of Irish-Cream Cream-Soda and age. The data is provided below. Conduct the appropriate statistical test either by hand or via SPSS (listed at the bottom), record your answers on the answer sheet, and attach SPSS output.

ID

Age

Rating

1

48

1

2

48

4

3

26

8

4

24

3

5

24

7

6

23

10

7

23

9

8

33

6

9

33

5

10

30

5

11

29

5

12

26

10

13

41

3

14

40

2

15

35

3

a) State (0.5 pt) and calculate (0.5 pt) an acceptable measure of variability for Age? (1 pt)

b) What is the appropriate statistical test to answer question? (0.5 pt)

c) Step 1: What is your prediction regarding the results of the statistical test? (0.5 pt)

d) Step 2: Set up hypotheses (2 pts)

H0 (1 pt):   

H1 (1 pt):   

e) Step 3: Set criteria for decision (2 pts)

Critical value (1 pt):

Decision Rule (1 pt):   

f) Step 5: Report Results (2 pts) – Must include test statistic (0.5 pt), degrees of freedom (0.5 pt), p-value (0.5 pt), and appropriate measure of effect size (0.5 pt)

g) Step 6: Interpret the results of the statistical test in terms of the research question (1 pt)

SPSS DATA
(First Section = Age)
(Second Section = Rating)

48   1
48   4
26   8
24   3
24   7
23   10
23   9
33   6
33   5
30   5
29   5
26   10
41   3
40   2
35   3

In: Math

We performed a linear regression analysis between number of times on phone per drive and number...

We performed a linear regression analysis between number of times on phone per drive and number of near accidents. The equation is Y= 0.320 + 0.943X, where Y is the number of times on phone per drive and X is the number of near accidents. calculate the p-value and give a conclusion.

number of times on phone per dr near accidents
0 0
0 1
1 1
2 1
3 1
1 2
2 2
3 2
4 2
2 3
3 3
4 3
2 4
3 4
4 4
5 4
6 4
3 5
4 5
5 5
6 5
4 6
5 6
7 6
8 7
9 7

In: Math

Find the expected count and the contribution to the chi-square statistic for the left-parenthesis C comma...

Find the expected count and the contribution to the chi-square statistic for the left-parenthesis C comma F right-parenthesis cell in the two-way table below. Upper D Upper E Upper F Upper G Total Upper A 39 30 36 36 141 Upper B 77 88 70 55 290 Upper C 21 37 27 28 113 Total 137 155 133 119 544 Round your answer for the excepted count to one decimal place, and your answer for the contribution to the chi-square statistic to three decimal places. EXPECTED COUNT: CONTRIBUTION TO THE CHI-SQUARE STATISTICS:

In: Math

Complaints concerning excessive commercials seem to grow as the amount of “clutter,” including commercials and advertisements...

Complaints concerning excessive commercials seem to grow as the amount of “clutter,” including commercials and advertisements for other television shows, steadily increases on network and cable television. A recent analysis by Nielsen Monitor-Plus compares the average nonprogram minutes in an hour of prime time for both network and cable television. Data for selected years are shown as follows. Year 1996 1999 2001 2004 Network 9.88 14.00 14.65 15.80 Cable 12.77 13.88 14.50 14.92 a. Calculate the correlation coefficient for the average nonprogram minutes in an hour of prime time between network and cable television. b. Conduct a hypothesis test to determine if a positive correlation exists between the average nonprogram minutes in an hour of prime time between network and cable television. Use a significance level of 0.05 and assume that these figures form a random sample.

In: Math