Question

Student: Date: 11/14/19 Instructor: Assignment: Chapter 8 Homework Course: Elementary Statistics F19 10. Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative 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 beiow 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 ciaim that the sample is from a populalion with a mean less than 1000 hic. Do the results suggest that all of the child booster seats meet the specified requirement? 731 655 1223 615 567 451 What are the hypotheses? OA. Ha: 1000 hic H 1000 hic B. Ho: 1000 hic H: H 1000 hic C. Hn:1000 hic D. Ho: 1000 hic H1 H2 1000 hic H, 1000 hic Identify the test statistic. t= (Round to three decimal places as needed.) identify the P-value. The P value is (Round to four decimal places as needed.) State the final conclusion that addresses the original claim (1) Ho. There is (2) population with a mean less than 1000 hic, evidence to support the claim that the sample is from a What do the results suggest about the child booster seats meeting the specified requirement? C) A. The results are inconclusive regarding whether one of the booster seats could have a measurement that is greater than 1000 hic B. 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 C. 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. O D. The requirement is met since most sample measurements are less than 1000 hic. (1) O Fail to reject O Reject (2) Oinsufficient O sufficient

Answer 1

To test null hypothesis Ho :4 = 1000.0 against alternative hypothesis HĽ :< 1000.0 Let ī denotes the sample mean, s denotes the sample standard deviation and n denotes the sample size. Here, ã = 707.0000, s2 = 72627.2000, s = 269.4943, n = 6 The test statistic can be written as: Vnī – 1000.0) t = which under Ho follows a t distribution with n -1 df. We reject Ho at 0.05 level of significance if P-value < 0.05 or if tobs < -10.050.n-1 Now, The value of the test statistic = -2.663138 associated degrees of freedom = 5 The critical value = -2.015048 P – value = P(t5 < tobs) = P(t5 < -2.663138) = 0.022358 Since p-value < 0.05 and tobs <tcritical = -2.015048, so we reject Ho at 0.05 level of significance Hence, we can conclude that population mean is significantly less than 1000.0

Final conclusion - 1) Reject, 2) sufficient

ans-> D)