Researchers measured skulls from different time periods in an attempt to determine whether interbreeding of cultures occurred. Results are given below. Assume that both samples are independent simple random samples from populations having normal distributions. Use a0.05significance level to test the claim that the variation of maximal skull breadths in 4000 B.C. is the same as the variation in A.D. 150. nxs4000 B.C.30131.92mm5.16mmA.D. 15030136.92mm5.31mm Question content area bottomPart 1What are the null and alternative hypotheses? A.H0:σ21≠σ22H1:σ21=σ22 B.H0:σ21=σ22H1:σ21≠σ22This is the correct answer. C.H0:σ21=σ22H1:σ21<σ22 D.H0:σ21=σ22H1:σ21≥σ22Your answer is not correct.Part 2Identify the test statistic. F=1.061.06(Round to two decimal places as needed.)Part 3Use technology to identify the P-value. The P-value isenter your response here.(Round to three decimal places as needed.) What is the conclusion for this hypothesis test?

Solution: Given information: n1=30 Sample size of 4000 B.C n2=30 Sample size of A.D 150 s1= 5.16 Sample standard deviation of 4000 B.C s2= 5.31 Sample standard deviation of A.D 150 Part 1) The null and alternative hypothesis are Ho:σ12=σ22 VS Ha:σ12≠σ22 Option B is Correct Part 2) Test statistic F= s22s12 since s22>s12F= 5.3125.162F= 28.196126.6256=1.058985F= 1.06 Test statistic F=1.06 To find p value p value = 2*P(F> 1.06) p value= 0.876 From Excel Decision: Do not reject Ho since p value > α=0.05 Conclusion: There is insufficient evidence to he claim that the variation of maximal skull breadths in 4000 B.C. is the same as the variation in A.D. 150..

Answered: Researchers measured skulls from…

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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	n	x	s
4000 B.C.	30	131.92 mm	5.16 mm
A.D. 150	30	136.92 mm	5.31 mm

Question content area bottom

Part 1

What are the null and alternative hypotheses?

H0:

σ21≠σ22

H1:

σ21=σ22

H0:

σ21=σ22

H1:

σ21≠σ22

This is the correct answer.

H0:

σ21=σ22

H1:

σ21<σ22

H0:

σ21=σ22

H1:

σ21≥σ22

Your answer is not correct.

Part 2

Identify the test statistic.

F=1.061.06

(Round to two decimal places as needed.)

Part 3

Use technology to identify the P-value.

The P-value is

enter your response here.

(Round to three decimal places as needed.)

What is the conclusion for this hypothesis test?

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.

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