What is the Central Limit Theorem? Discuss an example of its application.

1) A survey was conducted that asked 1002 people how many books they had read in the past year. Results indicated that x=12.9 books and s=16.6 books. Construct a 99​% confidence interval for the mean number of books people read. Interpret the interval.

Was there discrimination on the Titanic? Were first-class passengers given greater
access to life boats?
The unsinkable liner Titanic collided with an iceberg on her maiden voyage
in 1912 and sank with great loss of life. On board were 1317 passengers, some of
whom had paid a very much higher fare than others for the voyage. A not very
subtle sub-text in the most recent Titanic movie was the notion that the first class
passengers survived at a higher rate than other passengers.
Imagine we can regard the first class passengers as a sample of the total population
on board at the time of the collision. There were 324 first class passengers of whom
62% survived the sinking. In other words our sample proportion p^ = 0:62 while n is
324. The proportion of survivors from the total population (all passengers) on board
was p = 0:38:
Using a 0.05 significance level, test whether the survival rate for first class passengers
was greater than that for all passengers. Do the six steps of the test.

Appraise what new statistical methods are used in the evaluation of conceptual theories outlining specific advantages these methods provide. Compare Structural Equation Modeling (SEM) techniques providing advantages of using SEM to other conventional methods outlining some of the various statistical techniques that SEM is able to perform. Evaluate sampling techniques used to conduct hypothetical studies and asses the benefits of each sampling method based on best fit to application. Critique validity and reliability methods for appropriate constructs and compare advantages and disadvantages of each method describing what methods to use with different operational techniques. Compare and evaluate factor analysis for confirmatory versus exploratory methods and assess when each is appropriate proving examples and application usages. Assess the differences of various regression analysis methods and demonstrate by examples what regression methods are most appropriate for different application. Finally discuss and recommend best statistical techniques and methods to operationally use for means comparisons, non parametric evaluation, bivariate correlation, ANOVAs, Chi Square, regression, and other techniques as appropriate. Assess the overall concept of statistical power, why it has import to statistical evaluations, and what SPSS contributes to statistical analysis in today’s research.

What are the two limitations of correlation when interpreting the data?

The average income of 15 families who reside in a large metropolitan East Coast city is $62,456. The standard deviation is $9652. The average income of 11 families who reside in a rural area of the Midwest is $60,213, with a standard deviation of $2009. At α = 0.05, can it be concluded that the families who live in the cities have a higher income than those who live in the rural areas? can u show detail..

Evaluate the given expression and express the results using the usual format for writing numbers (instead of scientific notation) 32^C2=

Companies that recently developed new products were asked to rate which activities are most difficult to accomplish with new products. Options included such activities as assessing market potential, market testing, finalizing the design, developing a business plan, and the like.

A researcher wants to conduct a similar study to compare the results between two industries: the computer hardware industry and the banking industry. He takes a random sample of 64 computer firms and 89 banks. The researcher asks whether “market testing” is the most difficult activity to accomplish in developing a new product. Forty-seven percent (47%) of the sampled computer companies and fifty-four percent (54%) of the banks respond that it is the most difficult activity. Use a significance level of .20 to test whether there is a difference in the responses to this question from these two industries.

H₀:                                                                                Level of significance (α):   α =

H_A:                                                                               Type test:     two-tailed    left tail      right tail

Specify the random variable and distribution to be used in this hypothesis test.

Calculate the p-value                                                          Draw a graph and show the p-value

Show your work and any calculator functions used.

Compare the p-value with α                             Decide to Reject or Fail to reject the null hypothesis                   

Conclusion. State your results in non-technical terms.

Consider a senior Statistics concentrator with a packed extracurricular schedule, taking five classes, and writing a thesis. Each time she takes an exam, she either scores very well (a least two standard deviations above the mean) or does not. Her performance on any given exam depends on whether she is operating on a reasonable amount of sleep the night before (more than 7 hours), relatively little sleep(between 4-7 hours, inclusive), or practically no sleep (less than 4 hours). When she has had practically no sleep, she scores very well about 30% of the time. When she has had relatively little sleep, she scores very well 40% of the time. When she has had a reasonable amount of sleep, she scores very well 42% of the time. Over the course of a semester, she has a reasonable amount of sleep 50% of nights and practically no sleep 30% of nights. What is her overall probability of scoring very well on an exam? What is the probability she had practically no sleep the night before an exam where she scored very well? Suppose that one day she has three exams scheduled. What is the probability that she scores very well on exactly two of the exams, under the assumption that her performance on each exam is independent of her performance on another exam? What is the probability that she had practically no sleep the night prior to a day when she scored very well on exactly two out of three scams?

Similar Tests - Facebook Friends: You want to test the following similar claims about the number of Facebook friends that college students have.

For each test, choose the appropriate null hypothesis.

(a) Claim: The average number of Facebook friends for college student users is greater than 254.
Choose the appropriate null hypothesis.

H₀: p = 254

H₀: p = 0.5    

H₀: x = 254

H₀: μ = 254

(b) Claim: Most college student Facebook users have more than 254 Facebook friends.
Choose the appropriate null hypothesis.

H₀: x = 254

H₀: p = 254    

H₀: μ = 254

H₀: p = 0.5

How to make a declie plot by using SAS?  

Solve following using Program R studio. Please show code and results. Thank you.

3. Assume that ? is a random variable represents lifetime of a certain type of battery which is exponentially distributed with mean 60 hours.  
a. Simulate 500 pseudorandom numbers (using set.seed(10)) and assign them to a vector called expran.
b. Calculate average of simulated data and compare it with corresponding theoretical value.
c. Calculate probability that lifetime is less than 50 hours using cumulative probability function.
d. Calculate the total lifetime for these 500 simulated lifetimes.
e. Calculate 80th percentile using quantile function.

A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 37 months and a standard deviation of 4 months. Using the 68-95-99.7 rule, what is the approximate percentage of cars that remain in service between 25 and 29 months? Do not enter the percent symbol. ans =

In the week before and the week after a​ holiday, there were
10 comma 00010,000
total​ deaths, and
49834983
of them occurred in the week before the holiday.
a. Construct a
9090​%
confidence interval estimate of the proportion of deaths in the week before the holiday to the total deaths in the week before and the week after the holiday.
b. Based on the​ result, does there appear to be any indication that people can temporarily postpone their death to survive the​ holiday?
a.
nothingless than<pless than<nothing
​(Round to three decimal places as​ needed.)

Standardized stock price indicators in three different countries over a week are listed below. An analyst is interested in knowing if the stock markets of these different countries are dependent on one another. The data set and a partial ANOVA table for this study are provided below. I II III 890 900 905 899 900 900 900 887 896 905 906 928 871 893 899 910 900 934 Source of variation SS DF MS F Treatment 748 2 374 ??? Error 2526 ??? ??? Total 3274 ???

Compute the MSE and the F statistic