Test whether the claim that the two sample groups come from populations with the same mean or not.

cistG
2021-10-17
Answered

Test whether the claim that the two sample groups come from populations with the same mean or not.

You can still ask an expert for help

irwchh

Answered 2021-10-18
Author has **102** answers

State the test hypotheses.

Let first population denote the treatment and the second population denote the placebo.

Null hypothesis:

$H}_{0}:{\mu}_{1}={\mu}_{2$

Alternative hypothesis:

$H}_{1}:{\mu}_{1}\ne {\mu}_{2$

Test statistic:

The test statistic formula is,

$t=\frac{({\stackrel{\u2015}{x}}_{1}-{\stackrel{\u2015}{x}}_{2})-({\mu}_{1}-{\mu}_{2})}{\sqrt{\frac{{s}_{p}^{2}}{{n}_{1}}+\frac{{s}_{p}^{2}}{{n}_{2}}}}$

Where$s}_{p}^{2}=\frac{({n}_{1}-1){s}_{1}^{2}+({n}_{2}-1){s}_{2}^{2}}{({n}_{1}-1)+({n}_{2}-1)$

With degrees of freedom$df={n}_{1}+{n}_{2}-2$

Let$\stackrel{\u2015}{x}}_{1$ denotes the first sample mean, $\stackrel{\u2015}{s}}_{1$ denotes the first sample standard deviation, $n}_{1$ denotes the first sample size, $\stackrel{\u2015}{x}}_{2$ denotes the second sample mean, $s}_{2$ denotes the second sample standard deviation, $n}_{2$ denotes the second sample size, $\mu}_{1$ denotes the first sample population mean, and $\mu}_{2$ denotes the second sample population mean.

The pooled sample variance is,

$s}_{p}^{2}=\frac{({n}_{1}-1){s}_{1}^{2}+({n}_{2}-1){s}_{2}^{2}}{({n}_{1}-1)+({n}_{2}-1)$

$=\frac{(22-1){\left(0.015\right)}^{2}+(22-1){\left(0.000\right)}^{2}}{(22-1)+(22-1)}$

$=\frac{0.004725+0}{42}$

$=0.0001125$

Substitute${n}_{1}=22{\stackrel{\u2015}{x}}_{1}=0.049,{s}_{p}^{2}=0.0001125,{n}_{2}=22$ and ${\stackrel{\u2015}{x}}_{2}=0.000$ in the test statistic formula

$t=\frac{(0.049-0.000)}{\sqrt{\frac{0.0001125}{22}+\frac{0.0001125}{22}}}$

$=\frac{0.049}{0.0032}$
###### Not exactly what you’re looking for?

Let first population denote the treatment and the second population denote the placebo.

Null hypothesis:

Alternative hypothesis:

Test statistic:

The test statistic formula is,

Where

With degrees of freedom

Let

The pooled sample variance is,

Substitute

asked 2020-11-01

Solve the following problems applying Polya’s Four-Step Problem-Solving strategy.

If six people greet each other at a meeting by shaking hands with one another, how many handshakes take place?

If six people greet each other at a meeting by shaking hands with one another, how many handshakes take place?

asked 2021-03-02

In how many ways can 7 graduate students be assigned to 1 triple and 2 double hotel rooms during a conference

asked 2020-11-09

Define Hypothesis testing and explain test of significance for small samples and large samples.

asked 2022-01-31

the row of numbers shown below to generate 12 random numbers between 01 and 99 09075 11123 14740 39704 88198 93469 52264 39270

asked 2021-03-05

For each of the following situations, state whether you’d use a chi-square goodness-of-fit test, a chi-square test of homogeneity, a chi-square test of independence, or some other statistical test:

a) Is the quality of a car affected by what day it was built? A car manufacturer examines a random sample of the warranty claims filed over the past two years to test whether defects are randomly distributed across days of the work week.

b) A medical researcher wants to know if blood cholesterol level is related to heart disease. She examines a database of 10,000 patients, testing whether the cholesterol level (in milligrams) is related to whether or not a person has heart disease.

c) A student wants to find out whether political leaning (liberal, moderate, or conservative) is related to choice of major. He surveys 500 randomly chosen students and performs a test.

a) Is the quality of a car affected by what day it was built? A car manufacturer examines a random sample of the warranty claims filed over the past two years to test whether defects are randomly distributed across days of the work week.

b) A medical researcher wants to know if blood cholesterol level is related to heart disease. She examines a database of 10,000 patients, testing whether the cholesterol level (in milligrams) is related to whether or not a person has heart disease.

c) A student wants to find out whether political leaning (liberal, moderate, or conservative) is related to choice of major. He surveys 500 randomly chosen students and performs a test.

asked 2021-01-24

What is the decision at a 0.05 level of significance for each of the following tests?

F(3, 26) = 3.00

Retain or reject the null hypothesis?

F(4, 55) = 2.54

Retain or reject the null hypothesis?

F(4, 30) = 2.72

Retain or reject the null hypothesis?

F(2, 12) = 3.81

Retain or reject the null hypothesis?

F(3, 26) = 3.00

Retain or reject the null hypothesis?

F(4, 55) = 2.54

Retain or reject the null hypothesis?

F(4, 30) = 2.72

Retain or reject the null hypothesis?

F(2, 12) = 3.81

Retain or reject the null hypothesis?

asked 2022-03-24

Given the set: {-1, 6,4,11,x, -7}, for what x would the mean of the set be 1?