Scenario: Imagine you are a researcher who is interested in studying whether sleep deprivation leads to increased reaction times (i.e., being slower) when driving. You randomly select a sample of 30 licensed drivers. Fifteen participants are randomly assigned to get 5 hours of sleep for three consecutive nights. The other 15 participants are randomly assigned to get 8 hours of sleep for three consecutive nights. For the purposes of this Assignment, assume that all participants sleep exactly the required amounts. After the third night, all participants take a driving simulation test that measures their reaction times.

Use SPSS to determine if amount of sleep is related to reaction time.

1. Explain whether the researcher should use an independent-samples t-test or a related-samples t-test for this scenario. Provide a rationale for your decision.
2. Identify the independent variable and dependent variable.
3. Knowing the researcher believes that people who sleep less will have slower reaction times, state the null hypothesis and alternate hypothesis in words (not formulas).
4. Explain whether the researcher should use a one-tailed test or two-tailed test and why.
5. Identify the obtained t value for this data set using SPSS and report it in your answer document.
6. State the degrees of freedom and explain how you calculated it by hand.
7. Identify the p value using SPSS and report it in your answer document.
8. Explain whether the researcher should retain or reject the null hypothesis. Provide a rationale for your decision. Are the results statistically significant?
9. Explain what the researcher can conclude about the relationship between amount of sleep and reaction times.

Data:

Reaction times in seconds for participants with 5 hours of sleep
0.22
0.25
0.27
0.25
0.24
0.28
0.24
0.3
0.25
0.21
0.28
0.23
0.29
0.25
0.29

Reaction times in seconds for participants with 8 hours of sleep
0.21
0.23
0.2
0.24
0.28
0.23
0.3
0.29
0.23
0.21
0.21
0.27
0.29
0.23
0.25

Assume that the distribution of starting salaries for newly qualified CA’s is approximately Normal and has a std deviation of $2,500. We have a random sample of 16 CA’s.

a) Find the probability that the std error (sample std deviation) > $3000.

b) Find the probability that the std error (sample std deviation) < $1500.

Use the R script to answer the following questions: (write down your answers in the R script with ##)

(1). Import FarmSize.csv to Rstudio. Use the correct function to build a linear regression model predicting the average size of a farm by the number of farms; Give the model a name (e.g. FarmSize_Model). Call the model name to inspect the intercept and slope of the regression model. Verify the answers in your manual calculation.

(2). Use the correct function to generate the residuals for the 12 examples in the dataset from the model. Create a residual plot, with x axis as independent variable and y axis as residual.

(3). Use the correct function to inspect SSE, Se and r². Write down the values for these measures. Verify the answers in your manual calculation.

(4). Use the correct function to inspect slope statistic testing result. What is the t value for the slope statistic testing? What is the p value? What is the statistical decision?

In a study of speed​ dating, male subjects were asked to rate the attractiveness of their female​ dates, and a sample of the results is listed below (1 =not attractive; 10 equals=extremely ​attractive). Construct a confidence interval using a 95% confidence level. What do the results tell about the mean attractiveness ratings of the population of all adult​ females?

7​, 8​, 2​, 8​, 4​, 4, 6​, 7​, 7​, 10​, 6​, 8

__< μ <__

(a) Find the exact probability of exactly 55 heads in 100 tosses of a coin.

(b) Estimate this probability using normal distribution. Compare your answers.

In order to compare the means of two populations, independent random samples of 400 observations are selected from each population, with the results found in the table to the right. Complete parts a through e.

Sample 1

x1 = 5,265

s1 = 157

Sample 2

x2 = 5,232

s2 = 203

a. use a 95% confidence interval to estimate the difference between the population means (u1 - u2). Interpret the confidence interval.

b. test the null hypothesis H0: (u1 - u2) = 0 versus the alternative hypothesis Ha:(u1 - u2) =/ 0. Give the significance level of the test, and interpret the result.

c. Suppose the test in part b was conducted with the alternative hypothsis Ha:(u1 - u2) > 0. How would your answer to part b change?

d. test the null hypothesis H0:(u1 - u2) = 30 versus Ha:(u1 - u2) =/ 30. Give the significance level, and interpret the result. Compare your answer to the test conducted in part b.

e. What assumptions are neccessary to ensure the validity of the inferential procedures applied in parts a - d?

Friedman and Rosenman (1974) classified people into two categories: Type A personalities and Type B personalities.  Type A's are hard-driving, competitive, and ambitious. Type B's are more relaxed, easy going people.  One factor that differentiates these two groups is the   chronically high level of frustration experienced by Type A's, especially when doing statistical analyses.  (Oftentimes Type A's have been known to suffer from numerical alexithymia.) To verify this aspect separate samples of Type A's and Type B's are obtained. The following frustration scores were obtained (note: the higher the score the greater the degree of frustration)

Type A                                    Type B

25                                            21

   23                                            16

   19                                            19

                                                    18    

Question: Calculate the estimate of the standard error of mean differences ___________

Please show all work so I may check my steps

1. The life insurance industry maintains that the average worker in Saskatoon has no more than $25,000 of personal life insurance.  You believe this to be too low.  You sample 100 workers in Saskatoon at random and find the sample average to be $26,650 of personal life insurance.  The population standard deviation is known to be $12,000.  Use α=0.05 throughout.

1. (6) Test your belief using a significance level of 5%.
2. (6)  Explain, in the context of this question, what is meant by a Type I error, a Type II error, and the power of the test?
3. (5)  If the true average for this population is in fact $30,000, what is the probability of committing a Type II error?  
4. (1) Calculate the power of the test.

Write an analysis (essay) for question

2) The table summarizes the results from an observational study that followed a random sample of 8,474 people for about four years. All participants were free from heart disease at the beginning of the study. The variable Anger categorizes participants as Low Anger, Moderate Anger, High Anger based on the Speilberger Trait Anger Scale test, which measures how prone a person is to sudden feelings of anger. CHD stands for coronary heart disease, which is a count of the people who had heart attacks or needed medical attention for heart disease during the study.

Research Question:

Does this data suggest that there is an association between anger and heart disease?

Your analysis will include the following:

A Statements of the research question

A description of the source of the data

A description of the variables used in the analysis

A contingency table (two-way table)

Calculations of relevant percentages

Answer to the question based on your analysis of the data.

An advertising agency that serves a major radio station wants to estimate the mean amount of time that the station's audience spends listening to the radio daily. From past studies, the standard deviation is estimated as 48 minutes. A. What sample size is needed if the agency wants to be 95% confident of being correct to within +/-5 minutes? A sample size of ____ listeners is needed. ( Round up to the nearest integer.) B. If 99% confidence is desired, how many listeners need to be selected? If 99% confidence is desired, ___listeners need to be selected. (Round up to the nearest integer.)

1. Given that the random variable X is normally distributed with a mean of 30 and a standard deviation of 5, determine the following: P(32.2 <X).

2. The pdf(probability distribution function) of a random variable X is given by f(x) = 3x^2 with support 0<x<1. Determine P(0.4 < X < 0.6).

Discuss the process of selecting problem areas and formulating research questions within qualitative research studies. Compare and contrast your response to qualitative research studies.

Not handwriting answer, please

In a word document, please answer the following questions:

Course Introduction of Biostatistics

Define the following terms:
correlation coefficient
scatter plot
bivariate relationship
Provide an example where the outlier is more important to the research than the other observations?
Identify when to use Spearman’s rho.

A microwave manufacturing company has just switched to a new automated production system. Unfortunately, the new machinery has been frequently failing and requiring repairs and service. The company has been able to provide its customers with a completion time of 6 days or less. To analyze whether the completion time has increased, the production manager took a sample of 36 jobs and found that the sample mean completion time was 6.5 days with a sample standard deviation of 1.5 days.

a) At a significance level of 0.10, test whether the completion time has increased.

b) Find and interpret a 99% confidence interval for the mean completion time.

As the Data Manager (DM) on the “TES-100” project, the CEO has decided to proceed with the study and wants you to consider using the new savvy company system of remote data entry/electronic data capture. Review the current literature (i.e. internet) regarding this topic and decide if this study would be RDE/EDC appropriate, then write a 2-3 page paper or 20-25 slides on why you have made the decision you have made including pros and cons.