re Women Getting Taller? A researcher claims that the average height of a woman

Question

re Women Getting Taller? A researcher claims that the average height of a woman aged 20 years or older is greater than the 1994 mean height of 63.7 inches, on the basis of data obtained from the Centers for Disease Con- trol and Prevention's, Advance Data Report, No. 347. She btains a simple random sample of 45 women and finds the sample mean height to be 63:9 inches. Assume that the population standard deviation is 3,5 inches., Test the re- searcher's claim using either the classical approach or the P-value approach at the = 0.05 level of significance.

Explanation / Answer

SOLUTION:

Ho: mu=63.7

Ha:mu> 63.7

alpha=0.05

test statistic:

z=sample mean-pop mean/samplesd/sqrt(n)

=63.9-63.7/3.5/sqrt(45)

z =0.383

z cal=0.383

Decsion Rule:

if Z cal > Zcrit reject Null Hypothesis.

if Z cal<Z crit ,fail to reject Null hypothesis.

Decsion:

here Z cal=0.383

Z crit for 95%=1.96

Z cal<Zcrit

Fail to reject Null hypothesis.

Accept Null hypothesis.
there is no sufficient evidence at 5% level of significance to support the claim that average height is greater than 63.9 inches

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