a) Calculate sample size, mean, SD for each group x1 (Survived) and x2 (Not survived).b) Let us denote μ1= mean for x1 (Survived) and μ2 = mean for x2 (Not survived). Calculate 95% confidence intervals for each μ1 and μ2.c) Calculate 95% confidence intervals for the difference of means μ1 − μ2.d) Do the test of the hypothesis H0 : μ1 = μ2 vs H1 : μ1 ≠ μ2.Use the significance level α = 0.05. e) Do the test of the hypothesisH0 : μ1 = μ2 vs H1 : μ1 < μ2.Use the significance level α = 0.01. f) Find β and the power of the test for the hypothesisH0 : μ1 − μ2 = 0 vs H1 : μ1 − μ2 = −3.at the significance level α = 0.01. Q1.Use the following R code to create the data and plot of Age by Survided. We will compare mean age ofsurvived and non-survived group.library(ggplot2)library (dplyr)library (tidyr)library(titanic)titanicData <- drop_na (titanic_train)head (titanicData)PassengerId Survived Pclass## 11## 2211## 3313## 441## 553## 671##NameSex Age SibSp Parch## 1Braund, Mr. Owen Harrismale 221## 2 Cumings, Mrs. John Bradley (Florence Briggs Thayer) female 38Heikkinen, Miss. Laina female 261## 3Futrelle, Mrs. Jacques Heath (Lily May Peel) female 35Allen, Mr. William HenryMcCarthy, Mr. Timothy J## 41## 5male 35## 6male 54##TicketFare Cabin Embarked## 1A/5 21171 7.2500S## 2PC 17599 71.2833C85## 3 STON/02. 3101282 7.9250S## 4113803 53.1000 C123S## 5373450 8.0500S## 617463 51.8625E46x1 <- titanicData$Age [titanicData$Survived=31]x2 <- titanicData$Age [titanicData$Survived==0]par (mfrow=c (2,1))hist (x1, main="Survived", breaks=30)hist (x2, main="Not Survived" , breaks=30) Survived20406080х1Not Survived204060x2FrequencyFrequency0 30

“Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Answered: a) Calculate sample size, mean, SD for…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

a) Calculate sample size, mean, SD for each group x1 (Survived) and x2 (Not survived).

b) Let us denote μ1= mean for x1 (Survived) and μ2 = mean for x2 (Not survived). Calculate 95% confidence intervals for each μ1 and μ2.

c) Calculate 95% confidence intervals for the difference of means μ1 − μ2.

d) Do the test of the hypothesis

H0 : μ1 = μ2 vs H1 : μ1 ≠ μ2.

Use the significance level α = 0.05.

e) Do the test of the hypothesis

H0 : μ1 = μ2 vs H1 : μ1 < μ2.

Use the significance level α = 0.01.

f) Find β and the power of the test for the hypothesis

H0 : μ1 − μ2 = 0 vs H1 : μ1 − μ2 = −3.

at the significance level α = 0.01.

Q1.
Use the following R code to create the data and plot of Age by Survided. We will compare mean age of
survived and non-survived group.
library(ggplot2)
library (dplyr)
library (tidyr)
library(titanic)
titanicData <- drop_na (titanic_train)
head (titanicData)
PassengerId Survived Pclass
## 1
1
## 2
2
1
1
## 3
3
1
3
## 4
4
1
## 5
5
3
## 6
7
1
##
Name
Sex Age SibSp Parch
## 1
Braund, Mr. Owen Harris
male 22
1
## 2 Cumings, Mrs. John Bradley (Florence Briggs Thayer) female 38
Heikkinen, Miss. Laina female 26
1
## 3
Futrelle, Mrs. Jacques Heath (Lily May Peel) female 35
Allen, Mr. William Henry
McCarthy, Mr. Timothy J
## 4
1
## 5
male 35
## 6
male 54
##
Ticket
Fare Cabin Embarked
## 1
A/5 21171 7.2500
S
## 2
PC 17599 71.2833
C85
## 3 STON/02. 3101282 7.9250
S
## 4
113803 53.1000 C123
S
## 5
373450 8.0500
S
## 6
17463 51.8625
E46
x1 <- titanicData$Age [titanicData$Survived=31]
x2 <- titanicData$Age [titanicData$Survived==0]
par (mfrow=c (2,1))
hist (x1, main="Survived", breaks=30)
hist (x2, main="Not Survived" , breaks=30)

Survived
20
40
60
80
х1
Not Survived
20
40
60
x2
Frequency
Frequency
0 30

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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