1. Use t and F to test for a significant relationship between HRS1 and age. Use α = 0.05 and make sure you know what hypotheses you are using to conduct the significance tests.
2. Calculate and interpret the coefficient of determination R². Based on this R², did the estimated regression equation provide a good fit? Briefly justify your answer. Hint: If you used Excel Regression Tool to answer part c, R² was reported with your output.
3. Use the estimated regression equation to predict the HRS1 for a 60 year old individual.

Please show work in Excel thank you

Problem Scenario: Following is a problem description. For all hypothesis tests, you MUST state the statistical test you are using and use the P-VALUE METHOD through Microsoft Excel to make your decision. Show all steps, calculations, and work. For confidence intervals there is a specific Excel tool for each interval.  Treat each part of the question as a separate problem -- we use the same data set but are answering different “research questions”.

Many parts of cars are mechanically tested to be certain that they do not fail prematurely. In an experiment to determine which one of two types of metal alloy produces superior door hinges, 40 of each type were tested until they failed. To evaluate how long hinges made with the different alloys would last, the number of openings and closings was observed and recorded (to the closest 0.1 million). Car manufacturers consider any hinge that does not survive 1 million openings and closings to be a failure., A statistician has determined that the number of openings and closings is normally distributed.

NOTE: use ONLY the P-value method for hypothesis tests.

Number of Openings and Closings

a.) Estimate with 90% confidence the difference in the number of openings and closings between hinges made with Alloy1 and hinges made with Alloy 2. Interpret the interval.

b.) The quality control manager is not only concerned about the openings and closings of the hinges but is also concerned about the proportion of hinges that fail. Can we infer at the 10% significance level that the proportion of hinges made with Alloy 2 that fail exceeds 18%?

1.A large government building has received a telephone call threatening that an explosive device has been placed somewhere in the building. The bomb squad has been called to check out the threat and they have ordered all occupants to leave the building. The bomb squad will check out the building and declare whether or not it is safe to renter. (a) State the null and alternate hypothesis that is facing the bomb squad. (b) state the type-I and type-II error in this situation (c) which error is more serious here and why?  

2. A manufacturer of drinking water filters claims that their cartridge last more than 300 liters before they have to be replaced. A consumer group wants to confirm this claim and selects a random sample of 60 cartridges for testing. The cartridges produce a sample average lifetime of 312 liters, and a sample standard deviation of 50 liters. Construct a null and alternate hypothesis that the consumer group should use to confirm the manufacturer’s claim. Based on the sample data, what can the group conclude? Use a 5% level of significance. Would your answer change if you used a 1% level of significance? Justify

Two fair dice are rolled and the outcomes are recorded. Let X denotes the larger of the two numbers obtained and Y the smaller of the two numbers obtained. Determine probability mass functions for X and Y, and the cumulative distribution functions for X and for Y. Present the two cumulative distribution functions in a plot. Calculate E (2X + 2Y −8).

According to a social media​ blog, time spent on a certain social networking website has a mean of 22 minutes per visit. Assume that time spent on the social networking site per visit is normally distributed and that the standard deviation is 7 minutes. Complete parts​ (a) through​ (d) below.

a. If you select a random sample of 25 ​sessions, what is the probability that the sample mean is between 21.5 and 22.5 ​minutes? ___ ​(Round to three decimal places as​ needed.)

b. If you select a random sample of 25 sessions, what is the probability that the sample mean is between 21 and 22 minutes? ___ ​(Round to three decimal places as​ needed.)

c. If you select a random sample of 144 ​sessions, what is the probability that the sample mean is between 15.5 and 16.5 ​minutes? ​____ (Round to three decimal places as​ needed.)

d. Explain the difference in the results of​ (a) and​ (c).

The sample size in​ (c) is greater than the sample size in​ (a), so the standard error of the mean​ (or the standard deviation of the sampling​ distribution) in​ (c) is

______ than in​ (a). As the standard error _______ values become more concentrated around the mean.​ Therefore, the probability that the sample mean will fall in a region that includes the population mean will always ______ when the sample size increases.

1. Don't use handwriting,please.

2. Don't copy and paste use your own words.

3. I need Reference link . (important)

Q1:What is the difference between a population and a sample in statistics? (in details)
Q2. How to interpret confidence intervals and confidence levels?(in details)
Q3. Why the p-value is important?(in details)

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 280 engines and the mean pressure was 5.2 pounds/square inch (psi). Assume the population standard deviation is 0.8. If the valve was designed to produce a mean pressure of 5.3 psi, is there sufficient evidence at the 0.01 level that the valve performs below the specifications? Step 2 of 6 : Find the value of the test statistic. Round your answer to two decimal places.

For a population with µ = 80 and σ = 20 what is the z-score corresponding to X=95?

Experiment 4

Dr. Brown wanted to observe the effects of music genre on surgical recovery time. Dr. Brown set up an experiment in which participants were randomly assigned to listen to one of three different genres of music (rap, metal, or country). Participants were patients who had just received liposuction; they listened to their assigned music genre for 2 hours each day until discharged from the hospital. Dr. Brown recorded the number of days the patients remained in the hospital. His results are shown below.

Using the data shown below, conduct the appropriate statistical test in SPSS to determine whether there is a statistically significant difference between any of the pairs of musical genres.

1. What is the design of this experiment?

Three-way between-subjects factorial design

Three-way within-subjects factorial design

One-way between-subjects factorial design

One-way within-subjects factorial design

2. What kinds of samples are being used in this experiment?

Independent samples

Dependent samples

Matched samples

3. In the blank space in the conclusion below, write the statistical results of the experiment you analyzed above in APA style:

Based on the results of a one-way ANOVA, music genre does have an effect on number of days to recover from surgery,_________.

The average final exam score for the statistics course is 78%. A professor wants to see if the average final exam score for students who are given colored pens on the first day of class is different. The final exam scores for the 11 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal. 81, 61, 81, 91, 84, 56, 64, 74, 79, 63, 82 What can be concluded at the the α α = 0.10 level of significance level of significance? For this study, we should use The null and alternative hypotheses would be: H 0 : H 0 : H 1 : H 1 : The test statistic = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is α α Based on this, we should the null hypothesis. Thus, the final conclusion is that ... The data suggest that the population mean final exam score for students who are given colored pens at the beginning of class is not significantly different from 78 at α α = 0.10, so there is statistically insignificant evidence to conclude that the population mean final exam score for students who are given colored pens at the beginning of class is different from 78. The data suggest the population mean is not significantly different from 78 at α α = 0.10, so there is statistically insignificant evidence to conclude that the population mean final exam score for students who are given colored pens at the beginning of class is equal to 78. The data suggest the populaton mean is significantly different from 78 at α α = 0.10, so there is statistically significant evidence to conclude that the population mean final exam score for students who are given colored pens at the beginning of class is different from 78.

According to a daily​ newspaper, the probability is about 0.74 that the favorite in a horse race will finish in the money​ (first, second, or third​ place). Complete parts​ (a) through​ (j) below.

a. In the next five ​races, what is the probability that the favorite finishes in the money exactly​ twice? The probability that the favorite finishes in the money exactly twice is 0.096.

b. In the next five ​races, what is the probability that the favorite finishes in the money exactly four​ times? The probability that the favorite finishes in the money exactly four times is 0.390.

c. In the next five ​races, what is the probability that the favorite finishes in the money at least four​ times? The probability that the favorite finishes in the money at least four times is 0.611.

d. In the next five ​races, what is the probability that the favorite finishes in the money between two and four ​times, inclusive?

The probability that the favorite finishes in the money between two and four ​times, inclusive, is ____.

​(Round to three decimal places as​ needed.)

A department store supervisor is concerned about customer service. To check if this is an issue, the supervisor randomly selected a sample of clerks from stores at three different locations (A, B, C). Then the supervisor records the number of returns associated with each clerk for a month. What can the supervisor conclude with an α of 0.05?

Conduct Tukey's Post Hoc Test for the following comparisons:

1 vs. 3: difference =

f) Conduct Scheffe's Post Hoc Test for the following comparisons:
1 vs. 2: test statistic =
1 vs. 3: test statistic =   

1. What is the 95% CI for the difference between the mean starting salaries of those who stay at least three years and those who leave before 3 years?  Can you say that you are 95% sure there is a difference?