The amounts a soft drink machine is designed to dispense for each drink are normally distributed, with a mean of 11.7 fluid ounces and a standard deviation of 0.2 fluid ounce. A drink is randomly selected.

(a) Find the probability that the drink is less than 11.6 fluid ounces.

(b) Find the probability that the drink is between 11.5 and 11.6 fluid ounces.

(c) Find the probability that the drink is more than 12 fluid ounces. Can this be considered an unusual event? Explain your reasoning.

Is a drink containing more than 12 fluid ounces an unusual event?

A survey commissioned by the Southern Cross Healthcare Group reported that 15 % of New Zealanders consume five or more servings of soft drinks per week. The data were obtained by an online survey of 2090 randomly selected New Zealanders over 15 years of age (a) What number of survey respondents reported that they consume five or more servings of soft drinks per week? You will need to round your answer. XX = (b) Find a 95% confidence interval ( ±±0.001) for the proportion of New Zealanders who report that they consume five or more servings of soft drinks per week. 95% confidence interval is from to (c) Convert the estimate of your confidence interval to percents ( ±±0.1) % to %

Forty professional aeronautics students enrolled in a psychology course were asked how many hours they had studied during the past weekend. Their responses are provided below.

11	2	0	13	5	7	1	8	12	11
7	8	9	10	7	4	6	10	4	7
8	6	7	10	7	3	11	18	2	9
7	3	8	7	3	13	9	8	7	7

For the data above, construct a frequency table and histogram. Evaluate the graphics.

Is the data normally distributed? If not, is it positively or negatively skewed? Is there kurtosis?

A transportation museum has a building on both sides of Interstate 64/Highway 40. A walkway across the highway connects the two parts of the museum. At one of the exhibits, radar devices are placed in the walkways so that visitors can clock the speeds of motorists on the highway below. Following are the recorded speeds of motorists on a Tuesday afternoon (4:00 - 4:10).

83	77	75	74	72	72	69	68	68	68
68	62	62	62	62	62	61	61	61	61
61	61	60	58	58	58	58	58	57	57
57	57	56	55	54	54	54	54	54	53
52	52	52	52	52	47	47	43	40	40

For the data above, construct a frequency table and histogram. Evaluate the graphics. Is the data normally distributed? If not, is it positively or negatively skewed? Is there kurtosis?

The following is part of regression output produced by Excel ( for Y vs X1 and X2):

Y

12.9 6.1 1.1 39.7 3.4 5.9 8.9 15 7.3

X1

0.9 0.8 1.0 0.3 0.4 0.7 0.71 0.5 0.9

X2

4.2 3.1 1.2 15.7 2.5 0.7 5.0 6.4 3.0

A) write out the estimated regression equation showing that depends on X1 and X2.

b)if. X1=0.58 and X2=7.0, what is the value predicted for y

c)write the number which is the standard error of the regressions

d) which of the above value is the value of coefficient of multiple determination

e) if asked to do a simpler analysis by using only one of the two variables X1 and X2, which variable would be used?

Regression and Correlation

X	Y
fresh	marine
147	444
139	446
160	438
99	437
120	405
151	435
115	394
121	406
109	440
119	414
130	444
110	465
127	457
100	498
115	452
117	418
112	502
116	478
98	500
98	589
83	480
85	424
88	455
98	439
74	423
58	411
114	484
88	447
77	448
86	450
86	493
65	495
127	470
91	454
76	430
44	448
42	512
50	417
57	466
42	496

1. What are the the values for "a" and "b"?

2. Pearson's correlation Coefficient value r ?

1. A sample of retailers reported that they had the following number of copies of statistics textbooks in inventory:

57, 81, 69, 84, 85, 79, 71, 74, 55.

1. What is the mean number of textbooks in inventory? (10/200 points)

2. What is the median number of textbooks in inventory? (10/200 points)

3. What is the range of the number of textbooks in inventory? (5/200 points)

4. The standard deviation is 10.98. What is the variance? (round to two decimals) (5/200 points)

2. Create a Box and Whisker Plot using the following data. Be sure to give the 5 quartiles. (15/200 points)

12, 20, 15, 17, 32, 21, 45, 15

A data table contains two variables. One is the 30-year fixed mortgage rate; it is measured as the best rate offered by a mortgage broker over the last 90 days. The second variable holds a column of integers, 1-40, that identify different brokers. The 40 largest mortgage brokers are included in the data table. The data will be used to understand lending practices of all mortgage brokers in the U.S. Please choose the correct answer from the brackets for the questions below:

Hint: Use pencil/paper to construct what the data table might look like.

• The mortgage rate variable is ["nominal", "ordinal", "numeric"]     .
• True or false: the coding convention of the mortgage rate variable is a rate or percentage. ["True", "False"]    
• How many labeling variables are in the data table? ["0", "1", "2"]     
• The periodicity of the observations is ["monthly", "quarterly", "weekly", "none of these is the correct answer"]  

x: 1.5, 1, .25, .5

y: 3.75, 2, 1, 1.75

1) what is the % variation in y explained by the regression

2) test the null hypothesis that the slope =0 with the alternative that slope is not =0 and using alpha =.01. write down the test p value and state your conclusion about the hypothesis.

Chapter 12:

1. What two reasons do we use for the F-Statistic for?

2. What is the critical F value for a hypothesis test with a sample from 5 populations with 20 observations total. Use a .05 significance level.

3. Given a calculated F value of 3.5, would you reject or fail to reject the null hypothesis with the critical F value from question 2?

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?