Use the t-distribution to find a confidence interval for a mean μ given the relevant sample results. Give the best point estimate for μ, the margin of error, and the confidence interval. Assume the results come from a random sample from a population that is approximately normally distributed.

A 95% confidence interval for μ using the sample results x= 94.6, s= 6.9, and n =42

Round your answer for the point estimate to one decimal place, and your answers for the margin of error and the confidence interval to two decimal places.

point estimate =

margin of error =

the 95% confidence interval =

Read the following description and then answer items 12 to 16: Researchers are interested in determining if there is a difference between two exercise regimens (A and B). The researchers think that the regimens may have differential effects on a treadmill test where the participants run to exhaustion.

12.Write the appropriate null hypothesis.

14. What is the dependent variable in this study?

16. Describe what happens if the researchers make a type II error.

Consider a manufacturing process that produces cylindrical component parts for the automotive industry. According to specifications, it is important that the process produces parts having a mean diameter of 5.0 millimeters. An experiment is conducted in which 100 parts produced by the process are selected randomly and the diameter measured on each part. It is known that the population standard deviation is 0.1. It was found that the sample mean diameter is 5.027 millimeters. The process engineer Mr. Tan would like to find out how likely is it that one could obtain a sample mean diameter of at least 5.027 with sample size n = 100, if the population mean µ = 5.0. Apply the concept of central limit theorem. Mr Tan claimed that “In only 7 in 1000 experiments, one would experience by chance a sample mean that deviates from the population mean by as much as 0.027.” Do you agree? Explain your reasoning.

So, I am conducting a research project and I have many categorical variables that I am trying to run crosstab and chi-square tests on. The only issue is that I only recieved 81 respondents so a lot of my questions have less than 5 people who selected one answer over another. I am unsure what to do. Do I state in my discussion section that due to there being a lack of respondents that I could not test for significance on many of my variables? Or, is there another test that I can run that I am not thinking of?

In a quiz show a uniformly random integer r between 1 and 10 is generated. Another, independent such random numbers will then be generated, but before that happens, you are invited to guess whether s will be greater than or less than r. If you are correct, then you win s pounds. If you lose (or if s = r) then you win nothing. (i) Clearly if r = 1 you should guess that s will be larger. And if r = 10 you should guess that s will be smaller. At which value of r should your strategy change from guessing s will be larger to guessing it will be smaller? (Your aim, as always, is to maximise your expected gain.) (ii) Suppose now that the range of possible values for r and s is 1, ... , N. Then in the limit as N tends to infinity the change of strategy should happen at a value of r of approximately N/k. Find the value of k.

The toco toucan, the largest member of the toucan family, possesses the largest beak relative to body size of all birds. This exaggerated feature has received various interpretations, such as being a refined adaptation for feeding. However, the large surface area may also be an important mechanism for radiating heat (and hence cooling the bird) as outdoor temperature increases. Here are data for beak heat loss, as a percent of total body heat loss from all sources, at various temperatures in degrees Celsius. [Note: The numerical values in this problem have been modified for testing purposes.]

The equation of the least-squares regression line for predicting beak heat loss, as a percent of total body heat loss from all sources, from temperature is: (Use decimal notation. Enter the values of the intercept and slope rounded to two decimal places. Use the letter ?x to represent the value of the temperature.)

?̂ =_____

Use the equation of the least‑squares regression line to predict beak heat loss, as a percent of total body heat loss from all sources, at a temperature of 2525 degrees Celsius. Enter your answer rounded to two decimal places.

beak heat as a percent of total body heat loss=beak heat as a percent of total body heat loss=_____%

What percent of the variation in beak heat loss is explained by the straight-line relationship with temperature? Enter your answer rounded to two decimal places.

percent of variation in beak heat loss explained by the equation=percent of variation in beak heat loss explained by the equation=_____%

Find the correlation ?r between beak heat loss and temperature. Enter your answer rounded to three decimal places.

?=_____

A safety light is designed so that the times between flashes are normally distributed with a mean of 5.00s and a standard deviation of 0.40s

a. Find the probability that an individual time is greater than 5.50s

b. Find the probability that the mean for 60 randomly selected times is greater than 5.50s

c. Given that the light is intended to help people see an​ obstruction, which result is more relevant for assessing the safety of the​ light?

At a certain university, 50% of all entering freshmen planned to major in a STEM (science, technology, engineering, mathematics) discipline. A sample of 36 freshmen is selected. What is the probability that the proportion of freshmen in the sample is between 0.482 and 0.580? Write the answer as a number to the 4th decimal (0.1234).

The intended steps are as follows:

Step 1: Check to see that the conditions np ≥ 10 and n(1− p) ≥ 10 are
both met. If so, it is appropriate to use the normal curve.
Step 2: Find the mean U_p and standard deviation a_p.
Step 3: Sketch a normal curve and shade in the area to be found.
Step 4: Find the area using the TI-84 PLUS.

the national collegiate athletic association requires colleges to report the graduation rates of their athletes. at one large university, 78% of all students who entered in 2004 graduated in six years. one hundred thirty seven of the 190 students who entered with athletic scholarship graduated . consider these 190 as a sample of all athletes who will be admitted under present policies. is there evidence at the 5% level that the the percentage of athletes who graduate is less than 78%?

1. List the conditions for the test you plan to use, explain how these conditions are met, calculate and write down the test statistic, and find the P-value.

2. based on your P-value, conclude in context

Acrylic bone cement is commonly used in total joint replacement to secure the artificial joint. Data on the force (measured in Newtons, N) required to break a cement bond was determined under two different temperature conditions and in two different mediums appear in the following table. Temperature Medium Data on Breaking Force 22 degrees Dry 100.6, 142.9, 194.8, 118.4, 176.1, 213.1 37 degrees Dry 303.3, 338.3, 288.8, 306.8, 305.2, 327.5 22 degrees Wet 386.4, 368.2, 322.6, 307.4, 357.9, 321.4 37 degrees Wet 363.6, 376.8, 327.7, 331.9, 338.1, 394.6 (a) Estimate the difference between the mean breaking force in a dry medium at 37 degrees and the mean breaking force at the same temperature in a wet medium using a 90% confidence interval. (Round your answers to one decimal place.) ( , ) (b) Is there sufficient evidence to conclude that the mean breaking force in a dry medium at the higher temperature is greater than the mean breaking force at the lower temperature by more than 100 N? Test the relevant hypotheses using a significance level of 0.10. (Use μhigher temperature − μlower temperature. Round your test statistic to two decimal places. Round your degrees of freedom to the nearest whole number. Round your p-value to three decimal places.) t = df = P =

John finds a bill on his desk. He has three options: ignore it and leave it on his own desk, move the bill over to his wife Mary's desk, or pay the bill immediately. The probability that he leaves it on his own desk is 0.6. The probability that he moves it to Mary's desk is 0.3. The probability that he pays the bill immediately is 0.1.

Similarly, if Mary finds a bill on her desk she can choose to leave it on her own desk, put it on John's desk, or pay it immediately. The probability that it remains on her desk is 0.6. The probability she moves it to John's desk is 0.1. The probability she pays it immediately is 0.3.

Once a bill is paid it will not return to either of the desks. In other words, there is a 0% chance that a bill will return to John's desk or Mary's desk once it goes to the mailbox.

Assume this is a Markov Chain process. Set up the transition matrix and use it to answer the following questions. (Hint: When determining what your matrix labels should be, think of the location of the bill, not the action done to it. For example, the label "moves to the other desk" would not be a valid label.)

(a) What is the probability that a bill currently on John's desk will be paid within two days?


(b) What is the probability that a bill currently on John's desk will be on Mary's desk 3 days later?

a) The research firm suggests that they should do a hypothesis test for Eropa. Why might this be a reasonable approach to take? State and explain the appropriate null and alternative hypotheses. (COMPANY DETAILS GIVEN IN THE END OF THE QUESTIONS)

b) Describe what a type 1 error and what a type 2 error would be in the context of this problem. Describe the consequences of each of these types of errors.

c) Eropa remembers that when she took Statistics 101 (she has a BA in Psychology) for some reason a significance level of 5% was always used for hypothesis tests. Explain to Eropa why she might not want to automatically use 5%. What factors should she consider when choosing the level of significance?

d) Getting firms to respond to a survey is expensive and usually requires some inducement for the respondent. The firm gives Eropa a flat price of $15,000 for 50 respondents to the survey (and a report) and $150 for each additional respondent. You don’t have enough information to tell Eropa what sample size she should use but please describe for her what factors she should consider when deciding how big a sample to buy.

DETAILS OF THE COMPANY:

Eropa, an entrepreneur, created a company that matches firms (hotels, conference centres, etc.) that need to hire temporary staff for events (weddings, galas, conference dinners, etc.) to people looking for temporary work. Most hotels do not have enough permanent staff for these large, occasional events so they rely on temporary staff. There are temp agencies that connect these employers with bartenders, servers and others wanting to pick up extra shifts; in fact Eropa used to work for one of those agencies. Eropa has created an online platform (analogous to Airbnb or Uber) to match employers and employees and she is successfully disrupting temp agencies in eastern Canada. Eropa is considering expanding to Western Canada but it won’t be cheap (she figures she needs $1.5 million if she expands) so she wants to get a sense of market demand first. Eropa knows that there are about 10,000 firms that stage events in Western Canada that might need to hire temporary staff. She figures that if each firm, on average needs to fill at least 500 shifts a year with temporary staff there will be enough demand to justify entering the market. So, since there is no publically available data on current demand, she hires a market research firm to survey a sample of the 10,000 firms to estimate average demand for temporary staff (in shifts per year).

Name the ways in which the correlation coefficient can be interpreted.

1.The following is a chart of 25 baseball players' salaries and statistics from 2016.

In order to have correlation with 95% confidence (5% significance), what is the critical r-value that we would like to have?  

(Round to three decimal places for all answers on this assignment.)

RBI vs. Salary

Complete a correlation analysis, using RBI's as the x-value and salary as the y-value.

Correlation coefficient:

Regression Equation: y=

Do you have significant correlation? Select an answer Yes No

HR vs. Salary

Complete a correlation analysis, using HR's as the x-value and salary as the y-value.

Correlation coefficient:

Regression Equation: y=

Do you have significant correlation? Select an answer Yes No   

AVG vs. Salary

Complete a correlation analysis, using AVG as the x-value and salary as the y-value.

Correlation coefficient:   

Regression Equation: y=   

Do you have significant correlation? Select an answer Yes No

Prediction

Based on your analysis, if you had to predict a player's salary, which method would be the best? Select an answer Regression equation with RBI's Regression equation with HR's Regression equation with AVG The average of the 25 salaries

Using that method, predict the salary for Matt Wieters. His stats were:

RBI: 66

HR: 17

AVG: 0.243

Based on your analysis, his predicted salary would be: $ million  

His actual salary was $15.800 million.

2.

The following is data for the first and second Quiz scores for 8 students in a class.

Predict the value of the second quiz score if a student had a score of 14 on the first test. _

3-The following data were collected in a survey of 8th graders and summarize their cell phone status.

a) What proportion of the 8th graders have cell phones?

b) What proportion of the boys do not have cell phones?

c) What proportion of smart phone users are boys?