The upcoming championship high school football game is a big deal in your little town. The problem is, it is being played in the next biggest town, which is two hours away! To get as many people as you can to attend the game, you decide to come up with a ride-sharing app, but you want to be sure it will be used before you put all the time in to creating it. You determine that if more than three students share a ride, on average, you will create the app.

You conduct simple random sampling of 20 students in a school with a population of 300 students to determine how many students are in each ride-share (carpool) on the way to school every day to get a good idea of who would use the app. The following data are collected:

6 5 5 5 3 2 3 6 2 2

5 4 3 3 4 2 5 3 4 5

Construct a 95% confidence interval for the mean number of students who share a ride to school, and interpret the results.

Part A: State the parameter and check the conditions.

Part B: Construct the confidence interval. Be sure to show all your work, including the degrees of freedom, critical value, sample statistics, and an explanation of your process.

Part C: Interpret the meaning of the confidence interval.

Part D: Use your findings to explain whether you should develop the ride-share app for the football game.

In a psychology experiment reported in American Statistician , 25 female students completed a questionnaire measuring their fear of negative evaluation ("FNE" – a higher score indicates greater fear of negative evaluation). Eleven of the students were known to suffer from the eating disorder bulimia. The FNE scores are given here (scores of the bulimia sufferers in the top row).
10 13 13 14 16 19 20 21 21 24 25   
6 7 8 10 11 13 13 15 16 18 19 19 20 23
1. What parameter did the psychologists investigate? In which populations? What seems to be the point of this investigation?
2. Compute the mean FNE score in each sample. Which group appears to have the higher average FNE scores?
3. Use your calculator or other computational resource to verify these 95% confidence intervals for mean FNE scores:   
- students suffering from bulimia (14.5, 21.1)   
- students with normal eating habits (11.1, 17.2)
- Describe the procedures you used.
4. What assumptions are required for these intervals to be valid?
a) about the sample?
b) about the population?
5. Interpret each confidence interval with a sentence that begins "I'm 95% sure that..."
5. Would 90% confidence intervals be wider or narrower? Explain.
6. Notice that the two intervals overlap (the low end of the first interval is lower than the high end of the second interval). What does that say about the mean FNE scores of students in the two populations?

A measurement of a variable is said to be reliable when

Group of answer choices

it shows up on time to class

measures what it is believed to measure

it produces consistent results

none of the above

Question 6

For the next two questions consider the following research hypothesis: “Younger students will learn to use statistical software more quickly than older students.” What is the dependent variable?

Group of answer choices

age of students

number of computers previously purchased

time required to learn to use statistical software

presence or absence of math phobia

Question 7

What is the independent variable?

Group of answer choices

age of students

number of computers previously purchased

time required to learn statistical software

presence or absence of math phobia

Question 8

In order for a measurement to be valid it must also be reliable.

Group of answer choices

True

False

Question 9

What type of variable can theoretically assume any numerical value?

Group of answer choices

continuous

discrete

dichotomous

binary

Question 10

What do you call a continuous line that represents the frequency of scores within a class interval?

Group of answer choices

frequency polygon

line graph

histogram

tally marks

Question 11

If you wanted to examine the proportion of students in this class who is male compared to the proportion who is female, which of the following would be best suited to use?

Group of answer choices

ogive

line graph

pie chart

frequency polygon

Suppose we want to assess the effect of a one-day SAT prep class at a 5% level of significance. Scores on the SAT writing exam can range from 200 to 800. A random sample of 50 students takes the SAT writing test before and after a prep class. We test the hypotheses: LaTeX: H_0 H 0 : LaTeX: \mu=0 μ = 0 LaTeX: H_a H a : LaTeX: \mu>0 μ > 0 where LaTeX: \mu μ is the mean of the difference in SAT writing scores (after minus before) for all students who take the SAT prep class. The sample mean is 5 with a standard deviation of 18. Since the sample size is large, we are able to conduct the T-Test. The T-test statistic is approximately 1.96 with a P-value of approximately 0.028. What can we conclude? The one-day SAT prep class is associated with statistically significant improvements in SAT writing performance. Students taking a one-day SAT prep class performed significantly better on the SAT writing exam than students who did not take the class. Students taking a one-day SAT prep class do not show statistically significant improvements in their SAT writing performance. Scores only increased by 5 points, which is not significant on an exam where scores can range from 200 to 800. The one-day SAT prep class produces statistically significant improvements in SAT writing performance.

Problem 2) In absence of special preparation, according to the data from the College Board Web
site, half of students taking the SAT math exam scored above the national average. An educational
researcher was interested in the effectiveness of SAT coaching classes on improving SAT math
scores. Specifically, his study looked at whether a higher proportion of coached students scored
above the national average than for students who had not been coached. He selected a random
sample of 953 students who completed a coaching class prior to taking the SAT math exam and
noted how many scored higher than the national average score for the SAT math exam: 490 did
score higher than the average.
a) Consider just one experimental unit – that is, one student who completed the coaching class
prior to taking the math SAT. What is the response variable for that one student? Categorical or
quantitative?
b) The researcher wants to conduct a significance test to determine if SAT coaching classes are
associated with an increase in the proportion of students who score above the national average.
Verify the conditions for using the normal approximation for the sample proportion.
c) Conduct the significance test. Keep two nonzero digits in your calculation for ??̂ and for the
standard deviation. Sketch the distribution for ??̂ showing mean and area for P-value. State
your conclusion in plain English in the context of the problem. Look at the statements for
Problem 1 and use them as a guide.
d) Based on the conclusion of the significance test, would you recommend an SAT coaching class to
someone taking the SAT math exam? Why?

An education minister would like to know whether students at Gedrassi high school on average perform better at English or at Mathematics. Denoting by μ₁ the mean score for all Gedrassi students in a standardized English exam and μ₂ the mean score for all Gedrassi students in a standardized Mathematics exam, the minister would like to get a 95% confidence interval estimate for the difference between the means: μ₁ - μ₂.

A study was conducted where many students were given a standardized English exam and a standardized Mathematics exam and their pairs of scores were recorded. Unfortunately, most of the data has been misplaced and the minister only has access to scores for 4 students.

The populations of test scores are assumed to be normally distributed. The minister decides to construct the confidence interval with these 4 pairs of data points. This Student's t distribution table may assist you in answering the following questions.

a)Calculate the lower bound for the confidence interval. Give your answer to 3 decimal places.

Lower bound =

b)Calculate the upper bound for the confidence interval. Give your answer to 3 decimal places.

Upper bound =

An assistant claims that there is no difference between the average English score and the average Math score for a student at Gedrassi high school.

c)Based on the confidence interval the minister constructs, the claim by the assistant

be ruled out.

A study is done to determine if students in the California state university system take longer to graduate, on average, than students enrolled in private universities. One hundred students from both the California state university system and private universities are surveyed. Suppose that from years of research, it is known that the population standard deviations are 1.5231 years and 1 year, respectively. The following data are collected. The California state university system students took on average 4.6 years with a standard deviation of 0.8. The private university students took on average 4.2 years with a standard deviation of 0.3. Conduct a hypothesis test at the 5% level. NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

-state the null hypothesis

-state the alternative hypothesis

-In words, state what your random variable X_state − X_private  represents.

-State the distribution to use for the test. (Round your answers to two decimal places.)

X_state − X_{private ~ __ ( __ , __ )}

_-What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.)
-What is the p-value? (Round your answer to four decimal places.)
-Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value. (Upload your file below.)

-(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)
α =

-decision rejected or or do not reject

Read this paragraph from a student writer. Then work to:

Re-write the quote and the sentences surrounding it so that the paragraph includes a more successful “quote sandwich.”

In Tough’s point of view, students from low-income family take more time to graduate from a four year college. He said that “rich students graduate from college at much higher rates than low-income students do.” I agreed with his argument, I believe that the rate of graduation between rich student and poor students is high because almost all rich students don't have to work to pay for their college and have less problem on their mind to deal with. For example a lot of low-income student drop off from college due to problems happening in their lives like money and others. they can't handle working a full time job and manage school all at once, and still keep up with the his class mates. I am a full time worker so I know how difficult is to keep up with everything and complete all the school work. I get home tired and the only thing I want to do is sleep but I have to complete my school work so I create I school work time plan to help me keep organized and have all my work done on time.

Please include

Context before the quote, and re-statement and explanation after it