Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and altemative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.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 0.01 significance level to test the claim that thesample 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?674 566 1090 533 508 565 DWhat are the hypotheses?Ο Α. H, μ= 1000 hicΗ με 1000 hicO B. Ho: u> 1000 hicH: u< 1000 hicOC. Ho: u< 1000 hicO D. Ho: u= 1000 hicH: u2 1000 hicH:p< 1000 hicIdentify the test statistic.t= (Round to three decimal places as needed.)State the final conclusion that addresses the original claim.Ho. There isV evidence to support the claim that the sample is from a population with a mean less than 1000 hic.What do the results suggest about the child booster seats meeting the specified requirement?O A. The requirement is met since most sample measurements are less than 1000 hic.O B. There is strong evidence that the mean is less than 1000 hic, but one of the booster seatsa measurement that is greater than 1000 hic.O C. There is not strong evidence that the mean is less than 1000 hic, and one of the booster seats has a measurement that is greater than 1000 hic.O D. The results are inconclusive regarding whether one of the booster seats could have a measurement that is greater than 1000 hic.

Name: Assume that a simple random sample has been selected from a normally
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and altemative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original cl

Denote μ as the population mean hic measurement.Null hypothesis: H0: μ = 1,000. Alternative hypothesis: H1: μ < 1,000. Correct option is D. The sample size is n = 6. The degrees of freedom (df) for a one-sample t-test, for a sample of size n is (n – 1). Here, n = 6, so that df = 5. The test statistic is: t = (x̄ – μ) / (s/√n). Here, the sample mean is x̄ = 656. Thus, t = (656 – 1000) / (220/√6) = –344/89.8146239 ≈ –3.830. The test statistic is –3.830. Now, using the EXCEL formula =T.DIST(-3.830,5,TRUE) the p-value is obtained as approximately 0.0061. The level of significance is 0.01. Decision rule: If p-value is less than or equal to the level of significance, then reject the null hypothesis. Otherwise, failed to reject the null hypothesis. Conclusion: Here, the p-value of 0.0061 is less than the level of significance of 0.01. Thus, reject the null hypothesis. Reject H0. There is enough evidence to support the claim that the sample is from a population with a mean less than 1000 hic. Thus, 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. Correct option is B.