NASA is conducting an experiment to find out the fraction of people who black out at G forces greater than 6.

Suppose a sample of 1026 people is drawn. Of these people, 523 passed out. Using the data, construct the 99% confidence interval for the population proportion of people who black out at G forces greater than 6. Round your answers to three decimal places.

Please answer this using Rstudio

For the oyster data, calculate regression fits (simple regression) for the 2D and 3D data

a.1) Give null and alternative hypotheses

a.2) Fit the regression model

a.3) Summarize the fit and evaluation of the regression model (is the linear relationship significant).

a.4 )Calculate residuals and make a qqplot. Is the normal assumption reasonable?

Actual   2D   3D
13.04   47.907   5.136699
11.71   41.458   4.795151
17.42   60.891   6.453115
7.23   29.949   2.895239
10.03   41.616   3.672746
15.59   48.070   5.728880
9.94   34.717   3.987582
7.53   27.230   2.678423
12.73   52.712   5.481545
12.66   41.500   5.016762
10.53   31.216   3.942783
10.84   41.852   4.052638
13.12   44.608   5.334558
8.48   35.343   3.527926
14.24   47.481   5.679636
11.11   40.976   4.013992
15.35   65.361   5.565995
15.44   50.910   6.303198
5.67   22.895   1.928109
8.26   34.804   3.450164
10.95   37.156   4.707532
7.97   29.070   3.019077
7.34   24.590   2.768160
13.21   48.082   4.945743
7.83   32.118   3.138463
11.38   45.112   4.410797
11.22   37.020   4.558251
9.25   39.333   3.449867
13.75   51.351   5.609681
14.37   53.281   5.292105

(5) In a random sample of 21 ​people, the mean commute time to work was 31.5 minutes and the standard deviation was 7.3 minutes. Assume the population is normally distributed and use a​ t-distribution to construct a 80​% confidence interval for the population mean μ. What is the margin of error of μ​? Interpret the results.

(8) Use the standard normal distribution or the​ t-distribution to construct a 99​% confidence interval for the population mean. Justify your decision. If neither distribution can be​ used, explain why. Interpret the results. In a random sample of 17 mortgage​ institutions, the mean interest rate was 3.69​% and the standard deviation was 0.38​%. Assume the interest rates are normally distributed.

(3)

Construct the indicated confidence interval for the population mean μ using the​ t-distribution. Assume the population is normally distributed. c= 0.99​, overbar x=12.9​, s= 4.0​,n=5 round to one decimal place

Using the simple random sample of weights of women from a data​ set, we obtain these sample​ statistics:

nequals=4040

and

x overbarxequals=147.53

lb. Research from other sources suggests that the population of weights of women has a standard deviation given by

sigmaσequals=32.57

lb.

a. Find the best point estimate of the mean weight of all women.

b. Find a 95% confidence interval estimate of the mean weight of all women.

Refer to the accompanying data set of mean​ drive-through service times at dinner in seconds at two fast food restaurants. Construct a 95​% 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 Restaurant Y

80                   101

119                 125

118                 149

151                 117

268                 175

182                 137

120                 111

153                 126

164                 127

213                 123

329                 137

312                 133

182                 226

117                 209

154                 288

143                 128

101                 98

232                 136

240                 247

181                 140

149                 146

195                 202

168                 146

124                 139

69                   136

206                 143

177                 154

114                 138

139                 165

169                 134

193                 240

197                 235

235                 251

190                 237

354                 234

305                 172

206                 86

194                 104

184                 53

192                 172

102                 82

150                 140

174                 145

153                 98

173                 125

159                 146

170                 133

120                 184

135                 152

313                 132

Consider the following data for a dependent variable y and two independent variables, x₁ and x₂.

Round your all answers to two decimal places. Enter negative values as negative numbers, if necessary.

a. Develop an estimated regression equation relating y to x₁.

ŷ =_________ +___________ x₁

Predict y if x₁ = 45.

ŷ = ____________

b. Develop an estimated regression equation relating y to x₂.

ŷ =__________ +____________ x₂

Predict y if x₂ = 15.

ŷ = ___________

c. Develop an estimated regression equation relating y to x₁ and x₂.

ŷ =________ +___________ x1________ +____________ x2

Predict y if x₁ = 45 and x₂ = 15.

ŷ = __________

1. In order to evaluate a spectrophotometric method for the determination of titanium, the method was applied to alloy samples containing difference certified amounts of titanium. The results (%Ti) are shown below.

Sample                        Certified Value           Mean               Standard Deviation

1                      0.496                           0.482               0.0257

2                      0.995                           1.009               0.0248

3                      1.493                           1.505               0.0287

4                      1.990                           2.002               0.0212

For each alloy, eight replicate determinations were made. For each alloy, test whether the mean value differs significantly from the certified value.

Probability question please follow the comment

how do we use general inclusion and exclusion theorem to derive 4 to 5 events?

for example 3 events are that AUB=A+B-(A intersect B), but how about 4 and 5? Please you need to show me the step rather than paste the inclusion and exclusion formula and explain

A simple random sample of size

nequals=8181

is obtained from a population with

mu equals 73μ=73

and

sigma equals 18σ=18.

​(a) Describe the sampling distribution of

x overbarx.

​(b) What is

Upper P left parenthesis x overbar greater than 75.9 right parenthesisP x>75.9​?

​(c) What is

Upper P left parenthesis x overbar less than or equals 68.8 right parenthesisP x≤68.8​?

​(d) What is

Upper P left parenthesis 71 less than x overbar less than 77.8 right parenthesisP 71<x<77.8​?

Each week coaches in a certain football league face a decision during the game. On​ fourth-down, should the team punt the ball or go for a​ first-down? To aid in the​ decision-making process, statisticians at a particular university developed a regression model for predicting the number of points scored​ (y) by a team that has a​ first-down with a given number of yards​ (x) from the opposing goal line. One of the models fit to data collected on five league teams from a recent season was the simple linear regression​ model, E(y)=β0+β1x. The regression yielded the following​results: y=4.12−0.59x​, r squared equals 0.24.Complete parts a and b below.a.

Give a practical interpretation of the coefficient of​ determination, r2.

Choose the correct answer below.

A.Sample variations in the numbers of yards to the opposing goal line explain 24% of the sample variation in the numbers of points scored using the least squares line. This answer is correct.

B.There is a positive linear relationship between numbers of yards to the opposing goal line and numbers of points scored because 0.24 is positive.

C.There is little or no relationship between numbers of yards to the opposing goal line and numbers of points scored because 0.24 is near to zero.

D.Sample variations in the numbers of yards to the opposing goal line explain 76​%of the sample variation in the numbers of points scored using the least squares line.b. Compute the value of the coefficient of​ correlation, r, from the value of r2.

Is the value of r positive or​ negative? Why? Select the correct choice below and fill in the answer box within your choice. ​(Round to three decimal places as​ needed.)

A.The coefficient of​ correlation, r=________,is positive because the estimator of beta 1β1 is positive.

B.The coefficient of​ correlation,r=__________, is positive because the estimator of beta 1β1is negative.

C.The coefficient of​ correlation,r=___________,is negative because the estimator of beta 1β1is negative.

D.The coefficient of​ correlation,r=_________,is negative because the estimator of beta 1β1 is positive.

1. Calculate the covariance between profits and market capitalization and what does the covariance indicate about the relationship between profits and market capitalization? (positive or negative).

Identify the level of measurement of each of the following variables (Nominal, Ordinal, or Scale (Ratio):

1.  County names in a state

2. Number of participants in food stamp programs.

3. Reputations of colleagues ranked on the scale of Very High to Very Low.

4. Leadership ability measured on a scale from 0 to 5.

5. Divisions within a state agency.

6. Inventory broken down into three categories: tightly controlled, moderately controlled, or minimally controlled.

About 40% of all US adults will try to pad their insurance claims. Suppose that you are the director of an insurance adjustment office. Your office has just received 128 insurance claims to be processed int the next few days. What is the probability that -

half or more claims have been padded?

fewer than 45 of the claims have been padded:

From 40 to 64 of the claims have been padded?

More than 80 of the claims have not been padded?

The consumer food database contains five variables: Annual Food Spending per Household, Annual Household Income, Non-Mortgage Household Debt, Geographic Region of the U.S. of the Household, and Household Location. There are 200 entries for each variable in this database representing 200 different households from various regions and locations in the United States. Annual Food Spending per Household, Annual Household Income, and Non-Mortgage Household Debt are all given in dollars. The variable Region tells in which one of four regions the household resides. In this variable, the Northeast is coded as 1, the Midwest is coded 2, the South is coded as 3, and the West is coded as 4. The variable Location is coded as 1 if the household is in a metropolitan area and 2 if the household is outside a metro area. The data in this database were randomly derived and developed based on actual national norms.The consumer food database contains five variables: Annual Food Spending per Household, Annual Household Income, Non-Mortgage Household Debt, Geographic Region of the U.S. of the Household, and Household Location. There are 200 entries for each variable in this database representing 200 different households from various regions and locations in the United States. Annual Food Spending per Household, Annual Household Income, and Non-Mortgage Household Debt are all given in dollars. The variable Region tells in which one of four regions the household resides. In this variable, the Northeast is coded as 1, the Midwest is coded 2, the South is coded as 3, and the West is coded as 4. The variable Location is coded as 1 if the household is in a metropolitan area and 2 if the household is outside a metro area. The data in this database were randomly derived and developed based on actual national norms.

Provide a 1,600-word detailed, statistical report including the following:

• Explain the context of the case
• Provide a research foundation for the topic
• Present graphs
• Explain outliers
• Prepare calculations
• Conduct hypotheses tests
• Discuss inferences you have made from the results

This assignment is broken down into four parts:

• Part 1 - Preliminary Analysis
• Part 2 - Examination of Descriptive Statistics
• Part 3 - Examination of Inferential Statistics
• Part 4 - Conclusion/Recommendations

Part 1 - Preliminary Analysis (3-4 paragraphs)

Generally, as a statistics consultant, you will be given a problem and data. At times, you may have to gather additional data. For this assignment, assume all the data is already gathered for you.

State the objective:

• What are the questions you are trying to address?

Describe the population in the study clearly and in sufficient detail:

• What is the sample?

Discuss the types of data and variables:

• Are the data quantitative or qualitative?
• What are levels of measurement for the data?

Part 2 - Descriptive Statistics (3-4 paragraphs)

Examine the given data.

Present the descriptive statistics (mean, median, mode, range, standard deviation, variance, CV, and five-number summary).

Identify any outliers in the data.

Present any graphs or charts you think are appropriate for the data.

Note: Ideally, we want to assess the conditions of normality too. However, for the purpose of this exercise, assume data is drawn from normal populations.

Part 3 - Inferential Statistics (2-3 paragraphs)

Use the Part 3: Inferential Statistics document.

• Create (formulate) hypotheses
• Run formal hypothesis tests
• Make decisions. Your decisions should be stated in non-technical terms.

Hint: A final conclusion saying "reject the null hypothesis" by itself without explanation is basically worthless to those who hired you. Similarly, stating the conclusion is false or rejected is not sufficient.

Part 4 - Conclusion and Recommendations (1-2 paragraphs)

Include the following:

• What are your conclusions?
• What do you infer from the statistical analysis?
• State the interpretations in non-technical terms. What information might lead to a different conclusion?
• Are there any variables missing?
• What additional information would be valuable to help draw a more certain conclusion?

A group of high-school parents in Tucson, Arizona, in conjunction with faculty from the University of Arizona, claim that young women in the Tucson high schools not only are called on less frequently, but receive less time to interact with the instructor than do young men. They would like to see the school district hire a coordinator, spend money (and time) on faculty workshops, and offer young women classes on assertiveness and academic communication.

To make things simple, assume that instructor interactions with young men average 95 seconds, with standard deviation 35 seconds. (Treat this as population information.)

The null hypothesis will be that the average interaction time for young women will also be 95 seconds, as opposed to the alternate hypothesis that it is less, and will be tested at the 2.5% level of significance.

1. Give interpretations in context of Type I and Type II error in this situation. (Your discussion should not focus on “Null” and “Alternate”.)
2. What are the social, economic, and other consequences of (separately) Type I and Type II error?
3. Find the rejection region for this test. That is, what interaction time bounds the lower 2.5% of the distribution?
4. Assume the true mean interaction time for young women is 90 seconds. Find the power of the test.
5. Repeat part 4 for a true mean interaction time of 80 seconds.
6. What do the results in parts (4) and (5) mean in terms of your previous answers?