Answered: What is the null and alternate…

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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The following questions refer to the output below the following R command.

t.test(group1, mu = 30)

data: group1
t = -3.2893, df = 39, p-value = 0.002135

alternative hypothesis: true mean is not equal to 30
95 percent confidence interval:
24.03212 28.57704
sample estimates:
mean of x
26.30458

What is the null and alternate hypotheses
Which of the following assumptions need to be satisfied for this test?
1. Observations are independent
2. The standard deviations of both populations are normally distributed
3. The distributions of both populations are normal
4. The distribution of the population of differences is normal
5. The distribution of the population of measurements is normal
What is the value of the test statistic (4dp)
What is the p-value (4dp)
Based on this evidence, what is the conclusion

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution

Step 1

The t test is one of many tests used for the purpose of hypothesis testing in statistics.

1. Null and Alternative hypothesis are-

$H_{0} : μ = 30 H_{1} : μ \neq 30$

2. The following assumptions need to be satisfied for this test-

$O b s e r v a t i o n s a r e i n d e p e n d e n t T h e d i s t r i b u t i o n o f t h e p o p u l a t i o n o f m e a s u r e m e n t s i s n o r m a l . H e n c e o p t i o n (1) a n d (5) a r e c o r r e c t .$

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