Step 1 :Identify the null and alternative hypotheses. The null hypothesis (H0) is that the mean hic measurement is equal to 1000, while the alternative hypothesis (H1) is that the mean hic measurement is less than 1000.
Step 2 :Calculate the sample mean and standard deviation. The sample mean is 760.0 and the sample standard deviation is 254.1511361375353.
Step 3 :Calculate the test statistic using the formula for a one-sample t-test, which is (sample mean - population mean) / (sample standard deviation / sqrt(sample size)). The test statistic is -2.31.
Step 4 :Calculate the P-value using the t-distribution. The P-value is 0.0343.
Step 5 :Compare the P-value with the significance level (0.01). Since the P-value is greater than the significance level, we fail to reject the null hypothesis. This means that we do not have enough evidence to support the claim that the mean hic measurement is less than 1000.
Step 6 :Interpret the results in the context of the original claim. One of the booster seats has a hic measurement that is greater than 1000. This suggests that not all of the child booster seats meet the specified requirement.
Step 7 :The null and alternative hypotheses are: \(H_0\): \(\mu = 1000\) \(H_1\): \(\mu < 1000\)
Step 8 :The test statistic is \(\boxed{-2.31}\) and the P-value is \(\boxed{0.0343}\).
Step 9 :Since the P-value is greater than the significance level of 0.01, we fail to reject the null hypothesis. This means that we do not have enough evidence to support the claim that the mean hic measurement is less than 1000.
Step 10 :The results suggest that not all of the child booster seats meet the specified requirement. Therefore, the answer is \(\boxed{\text{A. There is strong evidence that the mean is less than 1000 hic, but one of the booster seats has a measurement that is greater than 1000 hic.}}\)