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). The safety requirement is that the hic measurement should be less than 1000 hic. Use a 0.05 significance level to test the claim that the sample is from a population with a mean less than 1000 hic. Do the results suggest that all of the child booster seats meet the specified requirement? 758       726       1204       639       584       463

Yes. There is enough evidence to support the claim that the sample is from a population with a mean less than 1000 hic.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the sample is from a population with a mean less than 1000 hic.

Then, the null and alternative hypothesis are:

The significance level is 0.05.

The sample has a size n=6.

The sample mean is M=729.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=255.

The estimated standard error of the mean is computed using the formula:

Then, we can calculate the t-statistic as:

The degrees of freedom for this sample size are:

This test is a left-tailed test, with 5 degrees of freedom and t=-2.6, so the P-value for this test is calculated as (using a t-table):

As the P-value (0.024) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the sample is from a population with a mean less than 1000 hic.