Question

A safety administration conducted crash tests of child booster seats for cars. Listed below are results from those tests, with the measurements given in hic (standard head injury condition units). 753 741 828 642 630 776 700 The safety requirement is that the hic measurement should be less than 770 hic. Use a 0.05 significance level to test the claim that the sample is from a population with a mean less than 770 hic.

(a). Express the original claim in symbolic form and state the null and alternative hypotheses

(b). Use the critical value approach or P− value approach to test the hypothesis.

c). Do the results suggest that all of the child booster seats meet the specified requirement?

Answer 1

a)

Claim: < 770

The null and alternative hypothesis

H0: >= 770

Ha: < 770

b)

From given sample data,

= X / n = 724.2857

S = sqrt [ X2 - n 2 / ( n -1) ] = 71.6303

Test statistics

t = ( - ) / (S / sqrt(n) )

= ( 724.2857 - 770) / ( 71.6303 / sqrt(7) )

= -1.69

From T table, t critical value at 0.05 significance level with 6 df = -1.943

Since test statistics t > -1.943, fail to reject H0.

c)

We do not have sufficient evidence to conclude that all of the child booster seats meet the

specified requirement.