Question

QUESTION 13

Some people claim that the physical demand on dancers are such that dancers tend to be shorter than the typical person. Nationally, adult heights are normally distributed with an average of 64.5 inches. A random sample of 20 adult dancers has an average height of 63.275 inches and a standard deviation of 2.17 inches. Is there evidence that dancers are shorter? Calculate the test-statistic for a test

Ho: μ = 64.5 versus Ha: μ < 64.5

Compute the test statistic for this test. (round your answer to 2 decimal places)

Answer 1

Here hypothesis is Ho: μ = 64.5 versus Ha: μ < 64.5

As n<30 and population standard deviation is not known, we will use t distribution to find the test statistics

Now P value is TDIST(2.52,19,1)=0.0104

As is not given let us assume it to be 0.05

As P value is less than we reject the null hypothesis

hence we have sufficient evidence to support the claim that dancers are shorter.