A watch designer claims that men have wrist breadths with a mean equal to 9 cm. A simple random sample of wrist breadths of 72 men has a mean of 8.91 cm. The population standard deviation is 0.36 cm. Assume a confidence level of a=0.01. Find the value of the test statistic z using z = xbar - sample meanxbar/popstandard deviation/sqrt n. Could anyone show me how to do this?

in Statistics Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

SAMPLE STATISTICS: mean wrist breadth (x bar)=8.91cm, size (n)=72 men.

POPULATION STATISTIC: standard deviation (σ)=0.36cm. 

CLAIM: Men have mean wrist breadths=9cm.

COUNTERCLAIM: Men have mean wrist breadths not equal to 9cm.

SIGNIFICANCE LEVEL: ɑ=0.01 (99% confidence level)

Null hypothesis, H₀: µ=9 (claim)

Alternative hypothesis, H₁: µ≠9(counterclaim)

This is a 2-tail test.

TEST STATISTIC: Z=(x bar-µ)/(σ/√n)=(8.91-9)/(0.36/√72)=-2.121, corresponding to a P-value of 0.017. Because we have a 2-tail test we compare this value with 0.005 because the tail probability is divided equally by the two tails. Since 0.017>0.005, we fail to reject the null hypothesis, so we have insufficient evidence to support or counter the claim.

by Top Rated User (645k points)

Related questions

Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
82,917 questions
87,575 answers
1,965 comments
4,220 users