In: Statistics and Probability

**1- Describe in detail who first introduced the
Confidence Intervals & Estimation process in Statistics, his
background and contribution to the field of
statistics?**

**2- Describe in detail a Confidence Interval Estimate is
a type of interval estimate that is computed from an observed
data?**

1)

Confidence intervals were introduced to statistics by Jerzy Neyman in a paper published in 1937

He was a Polish mathematician and statistician who spent the first part of his professional career at various institutions in Warsaw, Poland and then at University College London, and the second part at the University of California, Berkeley. Neyman first introduced the modern concept of a confidence interval into statistical hypothesis testingand co-revised Ronald Fisher's null hypothesis testing (in collaboration with Egon Pearson).

He published many books dealing with experiments and statistics, and devised the way which the FDA tests medicines today.

Neyman proposed and
studied randomized experiments in 1923. Furthermore, his paper "On
the Two Different Aspects of the Representative Method: The Method
of Stratified Sampling and the Method of Purposive Selection",
given at the Royal Statistical Society on 19 June 1934, was the
groundbreaking event leading to modern scientific sampling. He
introduced the confidence interval in his paper in
1937.^{[6]} Another noted contribution is the
Neyman–Pearson lemma, the basis of hypothesis testing.

2)

In statistics, a **confidence interval**
(**CI**) is a type of interval estimate, computed from
the statistics of the observed data, that might contain the true
value of an unknown population parameter. The interval has an
associated **confidence level** that, loosely
speaking, quantifies the level of confidence that the parameter
lies in the interval. More strictly speaking, the
**confidence level** represents the frequency (i.e.
the proportion) of possible confidence intervals that contain the
true value of the unknown population parameter. In other words, if
confidence intervals are constructed using a given confidence level
from an infinite number of independent sample statistics, the
proportion of those intervals that contain the true value of the
parameter will be equal to the confidence level.

for example t-test

Xbar and s , n are statistics based on sample

Describe in detail the Statisticians who first
introduced the “Hypothesis Testing”, their origin, background,
academic excellence and their further contribution in the field of
Statistics?

Describe in detail the Statisticians who first introduced the
“Hypothesis Testing”, their origin, background, academic excellence
and their further contribution in the field of Statistics?

1. Point vs. Interval Estimation
Here you will discuss the importance of constructing
confidence intervals for the population mean. You want to be sure
to address these questions:
What are confidence intervals?
What is a point estimate?
What is the best point estimate for the population
mean? Explain why it is the best.
Why do we need confidence intervals?
2. Mean Estimation
First clearly give the best point estimate for
the population mean the data was drawn from. Next you...

Let us use confidence intervals to compare people who own or are
buying a home among those that are married versus those who pay
rent among those that are married.
Calculate pˆ for the group of homeowners that are married.
For a confidence level of ell = .97, determine the z-score for
which 97% of normally
distributed data falls within z deviations of the mean.
Calculate pˆ for the group of renters that are married.
Now compare these two intervals....

1.
True or False: Confidence intervals can only be calculated for
means

Describe in detail the Confidence Interval consists of a range
of potential values of unknown population parameters?

Assignment 1 Part A - Confidence Intervals and Hypothesis
Testing
(One Population)
1. The shoulder height for a random sample of six (6) fawns (deer
less than 5 months old) in a national park was , ? = 79.25 cm with
population standard deviation ?= 5.33 cm. Compute an 80% confidence
interval for the mean shoulder height of the population of all
fawns (deer less than 5 months old) in this national park. Analyze
the result to interpret its meaning....

A rookie quarterback is in the process of negotiating his first
contract. The team's general
manager has offered him three possible contracts. Each contract
lasts for four years.
All of the money is guaranteed and is paid at the end of each
year. The payment
terms of the contracts are as follows:
(dollars in millions)
Year
Contract 1
Contract 2
Contract 3
1
$1.50
1.0
3.5
2
$1.50
1.5
0.5
3
$1.50
2
0.5
4
$1.50
2.5
0.5
The quarterback...

ANOVA was developed by statistician and evolutionary
Biologist Ronald Fisher, describe in detail his contribution in the
field of statistics?

1.) A confidence interval was used to estimate the proportion of
statistics students that are females. A random sample of 72
statistics students generated the following 90% confidence
interval: (0.438, 0.642). Which of the following interpretations is
correct?
Select one:
A. 90% of the sampled students are female.
B. We are 90% confidence that proportion of all statistics
female students falls in the interval 0.438 to 0.642
C. 90% of all statistic students are female.
D. We are 90% confident...

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