Question

Tests of Child Booster Seats The National Highway Traffic 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). The safety requirement is that the HIC measurement should be less than 1000 HIC. Use a 0.01 significance level to test the claim that the sample is from a population with a mean less than 1000 HIC. Write the hypothesis find test statistics and critical value. Use Test statistic t = -10.177.

602 696 762 572 637

Write your conclusion. Do you Reject the claim or Support the claim.

a) Reject H0, Fail to reject H1; Support the claim

b) H0: µ= 1000 ; H1: µ <1000 Test statistic t = 10.177 C.V. 3.747

c) Reject H0, Fail to reject H1; Reject the claim

d) H0: µ= 1000 H1: µ <1000 Test statistic t = -10.177 C.V. -3.747

Answer 1

Here in this scenario our claim is that the The safety requirement is that the HIC measurement is less than 1000 HIC.

To test this claim we have to use one sample t test because here the population standard deviations is unknown.

First we have to calculate the sample mean and standard deviations of sample as below,

The sample size is n = 5n=5. The provided sample data along with the data required to compute the sample mean \bar XXˉ and sample variance s^2s2 are shown in the table below:

	X	X2
	602	362404
	696	484416
	762	580644
	572	327184
	637	405769
Sum =	3269	2160417

The sample mean \bar XXˉ is computed as follows:

The t critical value is calculated using t table or using Excel at 4 degrees of freedom.

Conclusion : since p value is less than alpha level of significance so we Reject Ho null hypothesis and concluded that there is enough evidence to support claim that the Hic is less than 1000.

d) H0: µ= 1000 H1: µ <1000 Test statistic t = -10.177 C.V. -3.747

Thank you.