Use the sample information x¯ ⎯ x¯ = 40, σ = 7, n = 13 to calculate the following confidence intervals for μ assuming the sample is from a normal population.

(a) 90 percent confidence. (Round your answers to 4 decimal places.)
  
The 90% confidence interval is from __to__

(b) 95 percent confidence. (Round your answers to 4 decimal places.)
  
The 95% confidence interval is from __to__

(c) 99 percent confidence. (Round your answers to 4 decimal places.)
  
The 99% confidence interval is from __to__

(d) Describe how the intervals change as you increase the confidence level.
  

A- The interval gets narrower as the confidence level increases.

B- The interval gets wider as the confidence level decreases.

C- The interval gets wider as the confidence level increases.

D- The interval stays the same as the confidence level increases.

1.What elements define the position of the least squares regression line?

2.What are the parts of the regression equation? How do you interpret each?

3.What are the functions of the least squares regression equation?

4.Why is the slope an awkward measure of the strength of a relationship?

5.If the slope is zero, what is the value of r?

If x(overbar) =103 and sigma=8 and n=65 construct a 95% confidence interval estimate of the population mean, u

X is a binomial random variable.

n= 100 p= .4

Use the binomial approach and normal approximation to calculate the follwowing: 1. P(x>=38) 2. P(x=45) 3. P(X>45) 4. P(x <45)

The data below are for 30 people. The independent variable is “age” and the dependent variable is “systolic blood pressure.” Also, note that the variables are presented in the form of vectors that can be used in R. age=c(39,47,45,47,65,46,67,42,67,56,64,56,59,34,42,48,45,17,20,19,36,50,39,21,44,53,63,29,25,69) systolic.BP=c(144,20,138,145,162,142,170,124,158,154,162,150,140,110,128,130,135,114,116,124,136,142,120,120,160,158,144,130,125,175) a) Using R, develop and show a scatterplot of systolic blood pressure (dependent variable) by age (independent variable), and calculate the correlation between these two variables. b) Assume that these data are “straight enough” to model using a linear regression line. Develop and show that model (write out the model in the terms of the problem), and also show in a plot the line that best fits these data. c) Plot the residuals and comment on what you see as to how appropriate the model is. d) Using a boxplot, determine if there are any outliers in systolic blood pressure. If so, point out which points are outliers, if any. e) Assuming there is at least one outlier in systolic blood pressure, remove that outlier and re-do parts a) through c) again using the remaining data without the outlier(s). State and comment on this second model. f) In your second model, explain in the context of age and systolic blood pressure what the slope of your fitted line means. Also, for your second model, calculate R2 (the coefficient of determination), and explain what that means in the context of your second model.

Define the term “Historical Control” and explain its relevance to issues surrounding the differences between a “Randomized Controlled Experiment” and an “Observational Study”.

Explain the difference between a “quantitative variable” and a “qualitative variable” and give an example of each.

In the Ponderosa Development Corp. (PDC) example, if the land for each house costs $108,100 and lumber, supplies, and other materials cost another $41,200 per house. The company leases office and manufacturing space for $3,100 per month and their monthly salaries total to $65,250. Assume that total labor costs are approximately $26,800 per house. The cost of supplies, utilities, and leased equipment is $6,650 per month. The one salesperson of PDC is paid a commission of $3,900 on the sale of each house. The selling price of each house is $195,000.
(1) Identify all costs and revenue for each house.

(2) Write the monthly cost function c (x), revenue function r (x), and profit function p (x).

(3) What is the breakeven point (BEP) for monthly sales of the houses based on the cost, revenue and profit functions specified in (2)?

(4) What is the monthly profit if 13 houses per month are built and sold?

(5) What is the monthly profit if the variable cost per house = $160,500 and PDC built and sold 10 houses per month?

(4) What is the monthly profit if 13 houses per month are built and sold?

Suppose that 51% of all adults regularly consume coffee, 63% regularly consume carbonated soda, and 72% regularly consume coffee OR carbonated soda.

Note: Your answer must have both side of probability definition . Hint P (?) =?

(a) (5 points) What is the probability that a randomly selected adult regularly consumes both coffee and soda? Draw Venn diagram and label (with probability) each portion of the diagram to answer this question.

(b) (2 points) What is the probability that a randomly selected adult regularly consume at most one of these two products?

(c) (2 points) What is the probability that a randomly selected adult consume none these two products?

In the United States, voters who are neither Democrat nor Republican are called Independent. It is believed that 10% of voters are Independent. A survey asked 22 people to identify themselves as Democrat, Republican, or Independent.

A. What is the probability that none of the people are Independent? Probability =

B. What is the probability that fewer than 5 are Independent? Probability =

C. What is the probability that more than 17 people are Independent? Probability =

Suppose that 100 items are drawn from a population f manufactured products and the weight, X, of each item is recorded. Prior experience has shown that the weight has a right skewed probability distibution with mean=150 oz and standard deviation=30 oz. Find the value of X-bar for which P(X-bar > ?) = 0.75.

A project conducted by the Australian Federal Office of Road Safety asked people many questions about their cars. One question was the reason that a person chooses a given car, and that data is in table #11.2.8 ("Car preferences," 2013).

Table #11.2.8: Reason for Choosing a Car

Do the data show that the frequencies observed substantiate the claim that the reasons for choosing a car are equally likely? Test at the 5% level.

Refer to the accompanying data set of mean​ drive-through service times at dinner in seconds at two fast food restaurants. Construct a 90​% confidence interval estimate of the mean​ drive-through service time for Restaurant X at​ dinner; then do the same for Restaurant Y. Compare the results.

Restaurant X
84
118
121
149
267
184
120
155
166
211
336
311
173
109
159
153
98
237
237
180
158
200
167
122
60
197
175
113
140
175
191
203
233
196
352
306
211
193
183
185
105
149
173
157
176
152
168
123
139
305

Restaurant Y
99
126
149
121
173
133
106
120
127
128
133
134
231
212
290
123
93
133
239
141
142
202
144
140
141
145
159
132
166
132
242
232
246
239
230
165
85
105
50
170
73
142
138
103
125
144
130
180
151
125

When circuit boards used in the manufacture of compact disc players are tested, the long run percentage of defectives is 5%. suppose that a batch of 250 boards has been received and that the condition of any particular board is independent of that of any other board.

a) Calculate the exact probability that at least 10 of the boards in the batch are defective

b) Calculate the approx probability that at least 10 of the boards in the batch are defective using a normal distribution

(Please do these problems using a R software) this is a computer assignment (show work)

Data from a one-way layout are given below. Four treatments correspond to area sizes 0.016, 0.030, 0.044 and 0.058. You may regard them simply as treatments A, B, C and D.

(a) Construct the ANOVA table (follow lecture example to get all relevant quantities computed. Use a single line R-command only for verification).

(b) Use F-test for no difference in their means. State your statistical conclusion in a full sentence (e.g. the treatments are found statistically significantly different at 5% level).

(c) Carry out multiple comparisons for treatment differences (construct 95% simultaneous confidence intervals by the Tukey’s method).

data:

area velocity

0.016 294.9

0.016 294.1

0.016 301.7

0.016 307.9

0.016 285.5

0.016 298.6

0.016 303.1

0.016 305.3

0.016 264.9

0.016 262.9

0.016 256

0.016 255.3

0.016 256.3

0.016 258.2

0.016 243.6

0.016 250.1

0.03 295

0.03 301.1

0.03 293.1

0.03 300.6

0.03 285

0.03 289.1

0.03 277.8

0.03 266.4

0.03 248.1

0.03 255.7

0.03 245.7

0.03 251

0.03 254.9

0.03 254.5

0.03 246.3

0.03 246.9

0.044 270.5

0.044 263.2

0.044 278.6

0.044 267.9

0.044 269.6

0.044 269.1

0.044 262.2

0.044 263.2

0.044 224.2

0.044 227.9

0.044 217.7

0.044 219.6

0.044 228.5

0.044 230.9

0.044 227.6

0.044 228.6

0.058 258.6

0.058 255.9

0.058 257.1

0.058 263.6

0.058 262.6

0.058 260.3

0.058 305.3

0.058 304.9

0.058 216

0.058 216

0.058 210.6

0.058 207.4

0.058 214.6

0.058 214.3

0.058 222.1

0.058 222.2