STAT 250 GMU Confidence Interval for Proportion of Households Questions For doing Problem 1 please use regular Stat CrunchFor doing Problem 2 to 4 you need

STAT 250 GMU Confidence Interval for Proportion of Households Questions For doing Problem 1 please use regular Stat CrunchFor doing Problem 2 to 4 you need to go 1st groups then click Holland GMU STAT250 Spring 2020 then click 2nd page for doing the DA3 problems, you can see the data sets for DA3 problems 2,3 & 4For further information Please check the uploded file bellow…. STAT 250 Spring 2020 Data Analysis Assignment 3
Elements of good technical writing:
Use complete and coherent sentences to answer the questions.
Graphs must be appropriately titled and should refer to the context of the question.
Graphical displays must include labels with units if appropriate for each axis.
Units should always be included when referring to numerical values.
When making a comparison you must use comparative language, such as “greater than”, “less
than”, or “about the same as.”
Ensure that all graphs and tables appear on one page and are not split across two pages.
Type all mathematical calculations when directed to compute an answer ‘by-hand.’
Pictures of actual handwritten work are not accepted on this assignment.
When writing mathematical expressions into your document you may use either an equation
editor or common shortcuts such as:
x can be written as sqrt(x), p? can be written as p-hat, x
can be written as x-bar.
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Problem 1: Confidence Interval for Proportion of Households that have Amazon Prime (no
data set for this problem)
From a July 2019 survey of 889 randomly selected American households, it was discovered that
725 of them have an Amazon Prime membership.
a) Calculate the sample proportion of American households that have an Amazon Prime
membership. Round this value to four decimal places.
b) Write one sentence each to check the three conditions of the Central Limit Theorem.
Show your work for the mathematical check needed to show a large sample size was
taken.
c) Using the sample proportion obtained in (a), construct a 99% confidence interval to
estimate the population proportion of American households that have an Amazon Prime
membership. Please do this “by hand” using the formula and showing your work (please
type your work, no images accepted here). Round your confidence limits to three
decimal places.
d) Verify your result from part (c) using Stat ? Proportions Stats ? One Sample ? With
Summary. Inside the box, enter the number of successes, the number of observations,
and select confidence interval and click Compute! Copy and paste your StatCrunch
result in your document.
e) Interpret the StatCrunch confidence interval in part (d) in one sentence using the context
of the question.
f) Use the Confidence Interval applet (for a Proportion) in StatCrunch to simulate
constructing one thousand 99% confidence intervals assuming the proportion of
American households that have an Amazon Prime membership in the population is p =
0.82 and the sample size n = 889. Once the window is open, click reset and select (or
click) 1000 intervals. Copy and paste your full image into your document.
Box 1: Enter the given
population proportion, 0.82
Box 2: Enter the given
confidence level 0.99
Box 3: Enter the given
sample size, n = 889
g) Compare the “Prop. contained” value from part (f) to the confidence level associated with
the simulation in one sentence.
h) Write a long-run interpretation for your confidence interval method in context in one
sentence. Think about what happened above when you took many, many samples.
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Problem 2: Running a Mile
The Physical Fitness Test (PFT) is a comprehensive, health-related physical fitness battery of
tests for students in K – 12. One fitness area is Aerobic Capacity and is tested by having
students run one mile. In a particular county in Virginia, a sample of juniors in high school was
collected and presented in the data set called “Running a Mile.” If the student ran the mile in
less than 10 minutes, they passed this portion of the test (and is recorded as a “1” in the data set).
a) Obtain the sample proportion of students who “took less than 10 minutes” to run the mile
by using Stat ? Tables ? Frequency in StatCrunch. Show the full calculation of the
sample proportion by including the number of students who passed this portion, the total
number of students sampled, and the value of the sample proportion. Present this sample
proportion as a decimal rounded to four decimal places.
A physical education teacher wanted to test whether her county’s students are falling below the
national proportion. It is known that the national proportion for high school juniors passing the
aerobic portion of the test (running a mile in less than 10 minutes) is 0.70. Using ? = 0.05, is
there sufficient evidence to conclude that less than 70% of students run one mile in less than 10
minutes? Conduct a full hypothesis test by following the steps below.
b) Define the population parameter in context in one sentence.
c) State the null and alternative hypotheses using correct notation.
d) State the significance level for this problem.
e) Check the three conditions of the Central Limit Theorem that allow you to use the oneproportion z-test using one complete sentence for each condition. Show work for the
numerical calculation. You can assume the population is large.
f) Calculate the test statistic “by-hand.” Show the work necessary to obtain the value by
typing all the steps needed and the resulting test statistic. Do not round while doing the
calculation. Then, round the test statistic to two decimal places.
g) Calculate the p-value using the standard Normal table and provide the answer. Use four
decimal places for the p-value.
h) State whether you reject or do not reject the null hypothesis and the reason for your
decision in one sentence.
i) Based on your above decision, state your conclusion in context of the problem (i.e.
interpret your results and/or answer the question being posed) in one or two complete
sentences.
j) Use StatCrunch (Stat ? Proportion Stats ? One Sample ? with Data) to verify your test
statistic and p-value. Note, a success is a “1.” Copy and paste this into your document.
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Problem 3: Kindergarten Reading Levels
The population of kindergarten students in a particular state is 15,292 individuals. One variable
of interest was their reading level measured at the halfway point of the student’s kindergarten
year (based on a 9-month school year). The data set is called “Kindergarten Reading Levels”
and, for example, a student’s score of 1.4 means their reading level is considered first grade
fourth month.
a) Graph the distribution of the population of levels using a relative frequency histogram.
Please use the width of 0.1 by entering 0.1 next to “Width” under “Bins:”. Properly title
and label this graph and copy it into your document.
b) Interpret the shape of the population distribution in one complete sentence.
c) Provide the proportion of individuals in the population who have of 1.4 or higher. You
can highlight the histogram to help obtain this value. You do not need to copy the
highlighted histogram back into your document.
d) Use StatCrunch to obtain the mean and standard deviation for the Reading Levels
variable by using Stat ? Summary Stats ? Columns. Copy the table and round the
mean and standard deviation to two decimal places. Are these calculations parameters or
statistics? Answer this question in one sentence.
e) Take one sample of size 6 from the population using Data ? Sample. Once in the box,
click on the column you want to sample from. Then, enter 6 for your sample size and
keep the number of samples as 1. Finally click Submit. Once you have your sample,
calculate the mean and standard deviation of this sample. Copy the table and round the
mean and standard deviation to two decimal places. Are these calculations parameters or
statistics? Answer this question in one sentence.
f) Does the sample mean calculated in (e) come from a normal sampling distribution?
Check the three conditions of the Central Limit Theorem using one complete sentence for
each condition.
g) Take one sample of size 26 from the population using Data ? Sample and calculate the
mean and standard deviation of this sample. Copy the table and round the mean and
standard deviation to two decimal places. Are these calculations parameters or statistics?
Answer this question in one sentence.
h) Does the sample mean calculated in (g) come from a normal sampling distribution?
Check the three conditions of the Central Limit Theorem using one complete sentence for
each condition.
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i) Calculate the probability that, in a random sample of 26, the mean reading level is 1.4 or
greater. First, draw a picture with the mean labeled, shade the area representing the
desired probability. Please take a picture of your hand drawn sketch and upload it to your
Word document (if you do not have this technology, you may use any other method (i.e.
Microsoft paint) to sketch the image). Then, complete the problem by standardizing and
using the Standard Normal Table to obtain this probability. You must type the rest of
your “by hand” work to earn full credit.
j) Verify your answer in part (i) using the StatCrunch Normal calculator and copy that
image into your document. In addition, write one sentence to explain what the
probability means in context of the question.
k) Compare your result in (i) and (j) with the probability you obtained in part (c). Use this
comparison to comment on the difference between a population distribution and sampling
distribution.
Problem 4: Time it takes to Complete STAT 250 Exam 2
A random sample of 34 STAT 250 students was collected and the time it took them to complete
Exam 2 was recorded. The data was measured in minutes and the data set is called “Time to
Complete Exam 2.” The instructors of the course claim that the time it takes a student to
complete the exam will be different from 60 minutes. Consider the population of all times to be
left skewed. Using ? = 0.10, is there sufficient evidence to conclude that the mean time to
complete Exam 2 is different from 60 minutes? Conduct a full hypothesis test by following the
steps below. Enter an answer for each of these steps in your document.
a) Define the population parameter in context in one sentence.
b) State the null and alternative hypotheses using correct notation.
c) State the significance level for this problem.
d) Create a frequency histogram and a box plot of the sample data and copy these into your
document.
e) Check the conditions that allow you to calculate the test statistic in one to two sentences.
Was it necessary to consider the graphs of the sample data in part (d)?
f) No matter your results in part (d & e), calculate the test statistic “by-hand.” First,
calculate the sample mean and sample standard deviation using StatCrunch and do not
round these values. Next, show the work necessary to obtain the test statistic by typing
all your steps and providing the resulting test statistic. Do not round anything during the
calculation. Then, round the test statistic to three decimal places after you complete the
calculation.
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g) Use StatCrunch (Stat ? T Stats ? One Sample ? with Data) to verify your test statistic.
Copy and paste this box into your document.
h) State the p-value and the degrees of freedom using the output provided in part (g). Use
four decimal places for the p-value.
i) State whether you reject or do not reject the null hypothesis and the reason for your
decision in one sentence.
j) State your conclusion in context of the problem (i.e. interpret your results and/or answer
the question being posed) in one or two complete sentences.
k) Construct a 90% confidence interval using StatCrunch. Copy the output into your
document as your answer.
l) Explain the connection between the confidence interval and the hypothesis test in this
problem (discuss this in relation to the decision made from your hypothesis test and
connect it to the confidence interval you constructed in part (k)). Answer this question in
one to two sentences.
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To login Stat Crunch and finish the project please follow the direction below:
? For doing Problem 1 please use regular Stat Crunch
? For doing Problem 2 to 4 you need to go 1st groups
? then click Holland GMU STAT250 Spring 2020
? then click 2nd page for doing the DA3 problems, you can see the data sets for DA3
problems 2,3 & 4

Purchase answer to see full
attachment