1) Volatility (variation) of investment rates is an important consideration for investors. The following data represent the rate of return (%) for some mutual funds for the past 12 years, (like Sullivan, 5e, p 454, #16c). Determine the 95% confidence interval for the population standard deviation. 2 1 / 2 2 2 / 2 2 ( 1) / ( 1) /         n s n s (d.f. = n-1) 12.8 15.9 10.0 12.4 14.3 6.6 9.6 12.4 10.3 8.7 14.9 6.7

A) 2.2 < σ < 5.2

B) 2.3 < σ < 4.9

C) 3.2 < σ < 5. 6

D) 2.0 < σ < 5.9

Anyone who conducts and/or publishes research in the fields of economics, medicine, education, sociology, biology, criminal justice, psychology, (fill in your discipline here!), etc. is most likely not only familiar with the concept of a P-value, but has had research findings depend on it. Unfortunately, this is usually at the dismay of mathematicians and statisticians, as the P-value is not all it's cracked up to be. You will be investigated this for this week's discussion board.

1. In a brief paragraph, summarize what the P-value is, and how it is used to "strengthen" the findings in papers published in the fields listed above. Be sure to cite any sources that you pull from.
2. Search online for an article from the past 12 months that talks about how the P-value is misused, or if it should not be used anymore, or some other criticism of the use of the P-value method. Write a short paragraph summarizing the main points of the article, post the active link of the article so others can access it.
3. Present hypothesis testing problem (not from our textbook) that can be concluded using the P-Value method, But DO NOT solve it. A classmate will respond by solving your problem.

Researchers wondered if there was a difference between males and females in regard to some common annoyances. They asked a random sample of males and​ females, the following​ question: "Are you annoyed by people who repeatedly check their mobile phones while having an​ in-person conversation?" Among the

517

males​ surveyed,

155

responded​ "Yes"; among the 589

females​ surveyed,205

responded​ "Yes." Does the evidence suggest a higher proportion of females are annoyed by this​ behavior? Complete parts​ (a) through​ (g) below.

A statistics instructor is interested in examining the relationship between students’ level of statistics anxiety and their academic self-efficacy and statistics performance. A class of N = 10 students was asked to respond to a self-efficacy scale and an anxiety scale. Each student’s average statistics exam score was also recorded.

The results are as follows:

a. Explain what is meant by a correlation coefficient using one of the correlations as an example.

b. Study the table and comment on the patterns of results in terms of which variables are relatively strongly correlated and which are not very strongly correlated.

c. Comment on the limitations of making conclusions about direction of causality based on these data. In other words, discuss the issue of making cause-effect statements using correlations.

Last rating period, the percentages of viewers watching several channels between 11 p.m. and 11:30 p.m. in a major TV market were as follows:

Suppose that in the current rating period, a survey of 2,000 viewers gives the following frequencies:

(a) Show that it is appropriate to carry out a chi-square test using these data and calculate the value of the test statistic.

Each expected value is ≥        

χ2χ2        

Is your favorite TV program often interrupted by advertising? CNBC presented statistics on the average number of programming minutes in a half-hour sitcom. For a random sample of 20 half-hour sitcoms, the mean number of programming minutes was 23.36 and the standard deviation was 1.13. Assume that the population is approximately normal. Estimate with 97% confidence the mean number of programming minutes during a half-hour television sitcom.  (Round to 2 decimal places.)

Complete the following sentence to provide an interpretation of the confidence interval in the context of the problem:

We are 97% confident that the population mean number of programming minutes for all half-hour television sitcoms is between _______ and _________.

At a local business school, it is typical for some fraction of students to pass an Accounting certification exam. Recently, funding was used to develop a new program that was designed to increase the proportion of students who pass the exam. The school that developed this program studied 475 students and found that the percentage of students who passed the certification increased to 72% with a 95% confidence interval of [.68, .76]. The hypothesis test, H0: No improvement / same rate as always vs. H1: The intervention changed the passing rate, was rejected with a p-value of .046.  

1. Explain what the​ p-value means in this context.

   1. Someone says that they thought that the original pass rate was 67%. If that were true, what would you tell them about the efficacy of the program? Phrase the conclusion properly.

   2. If the alternative hypothesis had been, H1: The intervention increased the passing rate, would the p-value change? If so, how? Would you more or less strongly recommend adoption of the new program?   

   3. Even though this program has been shown to be better​ in that it is “statistically significant”, are there reasons that the school should not adopt it?

   4. What is the relationship between the p-value and the confidence interval?   

You wish to test the following claim ( H 1 ) at a significance level of α = 0.01 . For the context of this problem, μ d = μ 2 − μ 1 where the first data set represents a pre-test and the second data set represents a post-test. H o : μ d = 0 H 1 : μ d ≠ 0 You believe the population of difference in scores is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: pre-test post-test 47.7 -6.1 33.1 -10.7 57.2 65.3 51.3 63 38.2 23.4 68.8 31.6 27.7 22.3 37.2 50.3 34.2 3.3 72.6 45.4 What is the test statistic for this sample? (Report answer accurate to 2 decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to 4 decimal places.) p-value = The p-value is... less than (or equal to) α greater than α This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is not equal to 0. There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is not equal to 0. The sample data support the claim that the mean difference of post-test from pre-test is not equal to 0. There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is not equal

There is a 0.9968 probability that a female lives through the year. The cost of one year premium is $226. If she dies within the year the policy pays %50,000 in death benefit.

A. State the two events representing possible outcomes

B. Calculate the female's expected gain

450 policies are sold in one year. Let x = # of policyholders who die within the year.

C. Calculate the company's total intake from premiums for one year.

D. If the company is to make a profit, state the possible value(s) of x.

E. Find the probability that company makes a profit.

*Please show work, thank you*

A committee consists of six members (A, B, C, D, E, and F). A has veto power; B, C, D, and E each have one vote. F is a nonvoting member. For a motion to pass it must have the support of A plus at least two additional voting members. A weighted system that could represent this situation is:

Discuss the concept of researcher bias. What are some ways a researcher might address these issues?

Using the language R

Generate five random data sets that follow the normal random distribution with mean 5, variance 2. The sizes of these five data sets is 10, 100, 1000, 10000 and 100000. Draw the histogram, boxplot and QQ-plot (normal probability plot) of five data sets. Please make comments about these plots

An investigator wants to test whether exposure to secondhand smoke before 1 year of life is associated with development of childhood asthma (defined as asthma diagnosed before 5 years of age). Give two possible study designs and indicate the pros and cons of each. Then, provide your recommendation for the most efficient design.

Is there a relationship between confidence intervals and two-tailed hypothesis tests? Let c be the level of confidence used to construct a confidence interval from sample data. Let α be the level of significance for a two-tailed hypothesis test. The following statement applies to hypothesis tests of the mean.

For a two-tailed hypothesis test with level of significance α and null hypothesis H₀: μ = k, we reject H₀ whenever k falls outside the c = 1 − αconfidence interval for μ based on the sample data. When k falls within the c = 1 − α confidence interval, we do not reject H₀.

(A corresponding relationship between confidence intervals and two-tailed hypothesis tests also is valid for other parameters, such as p, μ₁ − μ₂, or p₁− p₂, which we will study later.) Whenever the value of k given in the null hypothesis falls outside the c = 1 − α confidence interval for the parameter, we reject H₀. For example, consider a two-tailed hypothesis test with α = 0.01 and

H₀: μ = 20        H₁: μ ≠ 20

A random sample of size 34 has a sample mean x = 23 from a population with standard deviation σ = 5.

(a) What is the value of c = 1 − α?


Construct a 1 − α confidence interval for μ from the sample data. (Round your answers to two decimal places.)

What is the value of μ given in the null hypothesis (i.e., what is k)?
k =  

Is this value in the confidence interval?

YesNo     

Do we reject or fail to reject H₀ based on this information?

We fail to reject the null hypothesis since μ = 20 is not contained in this interval.We fail to reject the null hypothesis since μ = 20 is contained in this interval.     We reject the null hypothesis since μ = 20 is not contained in this interval.We reject the null hypothesis since μ = 20 is contained in this interval.

(b) Using methods of this chapter, find the P-value for the hypothesis test. (Round your answer to four decimal places.)


Do we reject or fail to reject H₀?

We fail to reject the null hypothesis since there is insufficient evidence that μ differs from 20.We reject the null hypothesis since there is sufficient evidence that μ differs from 20.     We reject the null hypothesis since there is insufficient evidence that μ differs from 20.We fail to reject the null hypothesis since there is sufficient evidence that μ differs from 20.

Compare your result to that of part (a).

We rejected the null hypothesis in part (b) but failed to reject the null hypothesis in part (a).We rejected the null hypothesis in part (a) but failed to reject the null hypothesis in part (b).     These results are the same.

Body mass index (BMI) in children is approximately normally distributed with a mean of 24.5 and a standard deviation of 6.2. Answer the following questions: a) A BMI between 25 and 30 is considered overweight. What proportion of children are overweight? b) A BMI of 30 or more is considered obese. What proportion of children are obese? c) In a random sample of 10 children, what is the probability that their mean BMI exceeds 25?