A​ college's data about the incoming freshmen indicates that the mean of their high school GPAs was

3.5​,

with a standard deviation of

.20​;

the distribution was roughly​ mound-shaped and only slightly skewed. The students are randomly assigned to freshman writing seminars in groups of

25.

What might the mean GPA of one of these seminar groups​ be? Describe the appropriate sampling distribution​ model, including​ shape, center, and​ spread, with attention to assumptions and conditions. Make a sketch using the​ 68-95-99.7 Rule.

PLEASE USE R PROGRAMMING TO SOLVE THIS AND GIVE A COPYABLE CODE

Professor David teach Math 1054. In that course, there are 5 exams, 4 midterm exams, plus final exam. You are asked to help him to check whether there is significant difference among the difficulty level in these 5 exams. The data is stored in Math1054Exam.txt.

a). read in data (copy your R code)

b). Find averages for these exams. You can use mean(V) function, or summary(data) function.

c). Are these averages differ significantly? We need to use ANOVA. For this purpose, you need to use stack function to change the data format as two column, one is score, the

other is exam index.

d). Produce a boxplot for the five exams.

e). Conduct ANOVA test.

f). Copy your ANOVA table.

g). Make your conclusion.

------------------------------------------------------------------------------4

Math1054Exam.txt.

T1   T2   T3   T4   Final
90   69   62   65   92
67   59   78   63   43
76   73   66   41   71
80   92   46   92   70
98   79   60   84   99
82   80   69   83   94
69   45   47   70   37
83   90   54   66   50
93   94   90   94   99
66   67   50   52   32
45   71   55   58   83
76   92   65   72   95
73   92   84   70   77
81   68   30   53   34
60   58   43   50   36
92   90   86   89   95
62   54   52   60   88
85   80   65   82   88
69   80   81   67   75
71   88   43   61   89

You are a social worker in an OBGYN department of a hospital. The CEO of the hospital has asked you to write a report about the length of time that women spend in the hospital after giving birth. The CEO has told you that in the thinks that insured women spend longer on average in the hospital than uninsured women after childbirth. She wants you to test this claim with data from your hospital. Two samples of 16 women were taken. Test the claim that insured women spend longer in the hospital than uninsured women using an α = .01.

Insured:

Mean = 2.3 days

Standard Deviation = 0.77

Sample Size = 16

Uninsured:

Mean = 1.9 days

Standard Deviation = 0.77

Sample Size = 16

To complete this lab exercise, you should:

Identify whether you will test this claim using a 1-tailed hypothesis or a 2-tailed hypothesis.

State the Null and Research Hypotheses

Find the Critical Value using the T-Table and interpret what you will do with the null hypothesis given that Critical Value

Identify the Correct Degrees of Freedom you’ll use

HAND CALCULATE the t-value. Show your work. Start with the formula and then plug in the correct values from there.

Make a decision regarding the null. Interpret your decision with regard to this question.

Find the p-value range for the hypothesis test using your test statistic and the t-table.

BY HAND, construct a 98% Confidence Interval for the difference between insured and uninsured women. What does this confidence interval tell you?

What are your overall conclusions? Is the confidence interval interpretation consistent with your interpretation from the t-test?

The data shown below contains the monthly sales (in thousands of dollars) at a local department store for each of the past 24 months. Copy the data to Excel, perform a runs test, and compute a few autocorrelations to determine whether this time series is random. Give your conclusion by referring to the results of your runs test and autocorrelations (no need to try to attach the Excel output in this text box, just mention the specific values you refer to).

Please be sure to show all work to receive full credit. No credit will be given for an answer that is correct but has no work where it is necessary, or if the work showed does not logically equate to the given answer. No credit will be given for an incorrect answer with no work. Please try to answer all at one time.. please

1. The World Health Organization estimates that 5% of all adults in sub-Saharan Africa are living with HIV/AIDS. A survey takes a random sample of 1600 adults from all over sub-Saharan Africa and finds that 72 have HIV/AIDS.

a) What is the sample proportion and what is the population proportion?

b) What is the mean of the sampling distribution?

c) What is the standard deviation of the sampling distribution?

d) What is the probability that a random sample of 1600 adults in sub-Saharan Africa would have less than 4.5% living with HIV/AIDS?

2. In a random sample of 36 students at a college, the average IQ was x = 107. Assume that the IQ of a student in college follows a Normal distribution with unknown mean and standard deviation σ = 16.

a) Give a 90% confidence interval for μ.

b)Give a 99% confidence interval for µ.

c) Which confidence interval has a larger margin of error? Why does this make sense?

3) A researcher collects a random sample of size n from a population with standard deviation σ and, from the data collected, computes a 95% confidence interval for the mean of the population. Which of the following would produce a new confidence interval with a smaller width (smaller margin of error) based on these same data?
A. Increase σ.
B. Use a lower confidence level.
C. Use a smaller sample size.

Explain why you chose your answer.

B) The IQ scores for adults in the entire population have an approximately normal distribution with mean 100 and standard deviation 15. The researcher’s question in “Do college students aged 20 to 25 years old have a higher mean IQ than the rest of the population?” What are the appropriate null and alternative hypothesis a researcher would have to use if they chose to do an experiment to try to answer this question? Explain.

C) A survey on the number of hours spent working out was given to professors from the US. Assume the standard deviation of the number of hours spent by all professors in the US was found to be 1.94 hours. At a 98% confidence level, how many professors would have to be surveyed in order to bring the margin of error down to 0.1?

Sociologists say that 85% of married women claim that their husband's mother is the biggest bone of contention in their marriages (sex and money are lower-rated areas of contention). Suppose that ten married women are having coffee together one morning. Find the following probabilities. (For each answer, enter a number. Round your answers to three decimal places.)

(a) All of them dislike their mother-in-law. = 0.197

(b) None of them dislike their mother-in-law. = 0.00

(c) At least eight of them dislike their mother-in-law. =

(d) No more than seven of them dislike their mother-in-law. =

n a survey of a group of​ men, the heights in the​ 20-29 age group were normally​ distributed, with a mean of 68.6 inches and a standard deviation of 4.0 inches. A study participant is randomly selected. Complete parts​ (a) through​ (d) below. ​(a) Find the probability that a study participant has a height that is less than 66 inches. The probability that the study participant selected at random is less than 66 inches tall is ​(b) Find the probability that a study participant has a height that is between 66 and 71 inches. The probability that the study participant selected at random is between 66 and 71 inches tall is ​(c) Find the probability that a study participant has a height that is more than 71 inches. The probability that the study participant selected at random is more than 71 inches tall

1) Use worksheet “baseball stats” to perform a multiple regression analysis on the dataset found in BB2011 tab, using Wins as the dependent variable, and League, ERA, Runs Scored, Hits Allowed, Walks Allowed, Saves, and Errors as candidates for the independent variables. Perform the analysis at the 5% significance level.

a) Create a full write up, where you write your statistical analysis step by step. In your write up, make sure you address the following points.

·        Methodology and steps that you took to get to your final regression equation.

·        Final regression equation output.

·        What is the final regression equation?

·        Interpret all the coefficients in the equation.

·        Speak to whether the signs on the coefficients make sense.

·        Interpret R squared.

·        Include a full residual analysis.

·        What is the residual of the Tampa Bay observation?

b) Now, use tab BB2012 to make predictions of wins in 2012, using the model you created with the 2011 stats.  

·        How many games are the Giants (SFG) expected to win in 2012?

·        Which team is predicted by the model to have the worst record in 2012?

·        Which team is predicted by the model to have the best record in 2012?

Take a guess: if 1000 balls are dropped from the top, how will they be distributed in those slots in the bottom? Are they going to be distributed evenly at the bottom and form a horizontal line, or unevenly and form a roof-top shape, or something else? Jot down your guesses and your rationales. Go back to finish the video. 1. Share your initial guesses and final observations here. 2. If you agree it is a binomial distribution, what is the parameter n, and pi, in this case? (Hint: n is NOT the number of balls dropped.)

Below, n is the sample size, p is the population proportion of successes, and X is the number of successes in the sample. Use the normal approximation and the TI-84 Plus calculator to find the probability. Round the answer to at least four decimal places.

n=76, p=0.41

P(28<X<38) = ____?

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

A random sample of 5300 permanent dwellings on an entire reservation showed that 1690 were traditional hogans.

(a) Let p be the proportion of all permanent dwellings on the entire reservation that are traditional hogans. Find a point estimate for p. (Round your answer to four decimal places.)


(b) Find a 99% confidence interval for p. (Round your answer to three decimal places.)

Give a brief interpretation of the confidence interval.

1% of the confidence intervals created using this method would include the true proportion of traditional hogans.1
% of all confidence intervals would include the true proportion of traditional hogans.     
99% of all confidence intervals would include the true proportion of traditional hogans.
99% of the confidence intervals created using this method would include the true proportion of traditional hogans.

(c) Do you think that np > 5 and nq > 5 are satisfied for this problem? Explain why this would be an important consideration.

No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial.
Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal.     
Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial.
No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal.

A group of 51 college students from a certain liberal arts college were randomly sampled and asked about the number of alcoholic drinks they have in a typical week. The purpose of this study was to compare the drinking habits of the students at the college to the drinking habits of college students in general. In particular, the dean of students, who initiated this study, would like to check whether the mean number of alcoholic drinks that students at his college in a typical week differs from the mean of U.S. college students in general, which is estimated to be 4.73.

The group of 51 students in the study reported an average of 4.35 drinks per with a standard deviation of 3.88 drinks.

Find the p-value for the hypothesis test.  

The p-value should be rounded to 4-decimal places.

A company received a shipment from a supplier. The supplier company said the mean height of a tire is 21 inches and a standard deviation is 3 inches. The company is planning to choose 55 tires at random. What is the sample mean between 20 and 22? How many tires are likely to be taller than 25 iches?

Gru's schemes have a 9% chance of succeeding. An agent of the Anti-Villain League obtains access to a simple random sample of 1100 of Gru's upcoming schemes. Find the probability that... (Answers should be to four places after the decimal, using chart method, do NOT use the continuity correction):

...less than 101 schemes will succeed:

...more than 95 schemes will succeed:

...between 95 and 101 schemes will succeed:

...less than 8.5% of schemes will succeed:

...more than 9.5% of schemes will succeed:

...between 8.5% and 9.5% of schemes will succeed:

How are the population mean and the mean of the sampling distribution of the mean related?

-What is the standard error of the mean? What does it measure?

-What effect does increasing sample size have on the size of the standard error?

-What does the central limit theorem state?

-What are the units of a z-score?

-How are z-scores related to standard deviation and the mean?How are they interpreted?

-Is the α always a certain value, or is it up to the investigator?

-Is the p-value of a calculated statistic a designated number, or is it up to the investigator?

-How can we reduce Type I error?

-In hypothesis testing, how can you reach a decision about the null hypothesis by comparing yourcalculated statistic to the appropriate critical value?

-In hypothesis testing, how can you reach a decision about the null hypothesis by comparing the p-value from your calculated statistic to your alpha level?

-What is the interpretation of a confidence interval?

-What determines the width of a confidence interval? How is it affected by sample size and α?

-What do we use hypothesis testing to determine? What do we use confidence intervals to determine?

-When can we use z-tests and when do we have to, instead, use t-tests?

-How does the t-distribution compare to the z-distribution?

-What does it mean when two samples are “related”?

-Given two related samples, what are “repeated measures”? What are “matched pairs”?