Question

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?

Answer 1

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.