Assume that the differences are normally distributed. Complete parts ​(a) through ​(d) below. Observation 1 2 3 4 5 6 7 8 Upper X Subscript i 42.7 51.2 44.4 48.6 50.2 44.9 51.9 43.6 Upper Y Subscript i 46.6 49.6 48.6 52.7 50.6 47.4 52.4 45.7 ​(a) Determine d Subscript i Baseline equals Upper X Subscript i Baseline minus Upper Y Subscript i for each pair of data. compute d and sd test if Ud<0 at the 0.05 level of signifgance what is the pvalue reject or dont reject compute 95% confidence interval

Please show your work, thank you!

Which of the following are consequences of the Central Limit Theorem? I'm not sure why II and III are correct and the others are not.

I) A SRS of resale house prices for 100 randomly selected transactions from all sale

transactions in 2001 (in Toronto) will be obtained. Since the sample is large, we

should expect the histogram for the sample to be nearly normal.

II) We will draw a SRS (simple random sample) of 100 students from all University

of Toronto students, and measure each person’s cholesterol level. The average

cholesterol level for the sample should be approximately normally distributed.

III) We want to estimate the proportion of Ontario voters who intend to vote for the

Liberal party in the next election, and decide to draw a SRS of 400 voters. The

percentage of the people in the sample who will say that they intend to vote

Liberal is approximately normally distributed.

IV) We will draw a SRS of 100 adults from the Canadian military, and count the

number who have the AIDS virus. The number of individuals in the sample who

will be found to have the AIDS virus should be approximately normally

distributed.

V) We are interested in the average income for all Canadian families for 2001. The

mean income for all Canadian families should be approximately normal, due to

the large number of families in the population.

The local library if they get more patrons visiting by shifting some early morning hours to evening. They take a sample of days with morning hours included (8-5) compared to 12-9. Data below.

8am-5pm hours: 50, 40, 60, 60, 70, 35, 40 12-9 PM hours : 40, 80, 70, 60, 85, 90, 70

a) Provide null and alternative hypotheses in formal terms and layperson's terms for the t test for independent samples

b) Do the math and reject/accept at a=.05

c) Explain the results in layperson's terms

d) Calculate and explain a 95% confidence interval in layperson's terms if appropriate. If not, you must explain why not.

5. Two brands of coffee were compared. Two independent random samples of 50 people each were asked to taste either Brand A or Brand B coffee, and indicate whether they liked it or not. Eighty four percent of the people who tasted Brand A liked it; the analogous sample proportion for Brand B was ninety percent.

(A) [8] At α = 0.01, is there a significant difference in the proportions of individuals who like the two coffees? Use the p-value approach.

(B) [1] What is the critical value(s) for the test in Part(A)?

(C) [2] Construct a 99% confidence interval for the difference in the proportions of people who like Brand A and Brand B coffees.

(D) [2] Do we use the same estimate of the standard deviation of ˆp1 − pˆ2 in parts (A) and (C)? Explain.

Calories	BMI
1	2
2	4
3	5
4	4
5	5

What is the R-squared for this table and how do we interpret that?

A fair coin is tossed until the first head occurs. Do this experiment T = 10; 100; 1,000; 10,000 times in R, and plot the relative frequencies of this occurring at the ith toss, for suitable values of i. Compare this plot to the pmf that should govern such an experiment. Show that they converge as T increases. What is the expected number of tosses required? For each value of T, what is the sample average of the number of tosses required?

Describe the algorithm to generate random numbers from an arbitrary discrete distribution with finite number of outcomes.

• What is the level of significance? • What are Type I and Type II errors? • Interpreting and determining p-values • What is the relationship between sample size and power? • Understand the difference between a p-value and a confidence interval—strengths and weaknesses

What are the percentages of scores that fall between:

a) -1 and 0/0 and 1

b) -1 and -2/1 and 2

c) In the tails of a normal distribution.

• Define each type of variable: dichotomous, ordinal, categorical, continuous • Define the following study designs: Randomized controlled trial, prospective cohort study, case-control study, crossover study. • Define in dependent versus independent samples.

The following table is protein concentration in three groups of trypsin secretion.

<=50	51-1000	>1000
1.7	1.4	2.9
2	2.4	3.8
2	2.4	4.4
2.2	3.3	4.7
4	4.4	5
5	4.7	5.6
6.7	6.7	7.4
7.8	7.6	9.4
4	9.5	10.3

Perform ANOVA test BY HAND to test if there is a significant difference among these groups

7. The following data were collected in a clinical trial to compare a new drug to a placebo for its effectiveness in lowering total serum cholesterol. New Drug (n=75) Placebo (n=75) Total Sample (n=150) Mean (SD) Total Serum Cholesterol 182.0 (24.5) 206.3 (21.8) 194.15 (23.2) % Patients with Total Cholesterol < 200 78.0% 65.0% 71.5% a) Generate the 95% confidence interval for the difference in mean total cholesterol levels between treatments b) Generate a 95% confidence interval for the difference in proportions of all patients with total cholesterol < 200. c) How many patients would be required to detect the difference in proportions observed in the current study with a confidence interval of 95%.  

High daily temperatures and coffee sales (in hundreds of dollars) were recorded at a local Starbucks for eight randomly selected days. Results are listed in the table below. Is here a correlation between temperature and coffee sales? Use α=.05. What is the best predicted sales total for a day with a high temperature of 60° F?
x(° F) 32 39 51 60 65 72 78 81
y(hundreds of dollars) 26.2 24.8 19.7 20.0 13.3 13.9 11.4 11.2

r:
critical value:
Significant linear correlation? Yes or No?
Regression equation:
Best predicted time on 60° day:
What proportion of variation in sales is due to temperature?

The probability is 0.3 that a traffic fatality involves an intoxicated or​ alcohol-impaired driver or nonoccupant. In eight traffic​ fatalities, find the probability that the​ number, Y, which involve an intoxicated or​ alcohol-impaired driver or nonoccupant is a. exactly​ three; at least​ three; at most three. b. between two and four​, inclusive. c. Find and interpret the mean of the random variable Y. d. Obtain the standard deviation of Y.

Please answer form 6-14

I. Consider the random experiment of rolling a pair of dice. Note: Write ALL probabilities as reduced fractions or whole numbers (no decimals).

1) One possible outcome of this experiment is 5-2 (the first die comes up 5 and the second die comes up 2). Write out the rest of the sample space for this experiment below by completing the pattern:

1-1	2-1
1-2
1-3
1-4
1-5
1-6

2) How many outcomes does the sample space contain? _____________

3) Draw a circle (or shape) around each of the following events (like you would to circle a word in a word search puzzle). Label each event in the sample space with the corresponding letter. Event A has been done for you.

A: Roll a sum of 3.
B: Roll a sum of 7.
C: Roll a sum of at least 10.

D: Roll doubles.
E: Roll snake eyes (two 1’s). F: First die is a 4.

4) Find the following probabilities:
P(A) = _________ P(B) = _________ P(C) = _________

P(D) = _________ P(E) = _________ P(F) = _________

5) The conditional probability of B given A, denoted by P(B|A), is the probability that B will occur when A has already occurred. Use the sample space above (not a special rule) to find the following conditional probabilities:

P(D|C) = _________ P(E|D) = _________ P(D|E) = _________ P(A|B) = _________ P(C|F) = _________

6) Two events are mutually exclusive if they have no outcomes in common, so they cannot both occur at the same time.

Are C and E mutually exclusive? ___________
Find the probability of rolling a sum of at least 10 and snake eyes on the same roll, using the

sample space (not a special rule).
P(C and E) = __________

Find the probability of rolling a sum of at least 10 or snake eyes, using the sample space. P(C or E) = __________

7) Special case of Addition Rule: If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)

Use this rule to verify your last answer in #6:
P(C or E) = P(C) + P(E) = ________ + ________ = _________

8) Are C and F mutually exclusive? __________ Using sample space, P(C or F) = _________ 9) Find the probability of rolling a “4” on the first die and getting a sum of 10 or more, using the

sample space.
P (C and F) = ________

10) General case of Addition Rule: P(A or B) = P(A) + P(B) – P(A and B) Use this rule to verify your last answer in #8:

P(C or F) = P(C) + P(F) – P(C and F) = ________ + ________ − ________ = _________

11) Two events are independent if the occurrence of one does not influence the probability of the other occurring. In other words, A and B are independent if P(A|B) = P(A) or if P(B|A) = P(B).

Compare P(D|C) to P(D), using the sample space: P(D|C) = ________ . P(D) = ________ .
Are D and C independent? _________
When a gambler rolls at least 10, is she more or less likely to roll doubles than usual? ___________ Compare P(C|F) to P(C), using the sample space: P(C|F) = ________ . P(C) = ________ .

Are C and F independent? __________
12) Special case of Multiplication Rule: If A and B are independent, then P(A and B) = P(A) · P(B).

Use this rule to verify your answer to #9:
P(C and F) = P(C) • P(F) = ________ · ________ = ________ .

13) Find the probability of rolling a sum of at least 10 and getting doubles, using the sample space. P(C and D) = ________ .

14) General case of Multiplication Rule: P(A and B) = P(A) · P(B|A). Use this rule to verify your answer to #13:

P(C and D) = P(C) • P(D|C) = ________ · ________ = ________ .