A consumer researcher was asked to test a claim by a franchise swimming instruction program. Specifically, they claimed that they could teach the average 7-year-old to swim across an Olympic-size pool in less than 2 hours (120 minutes is the \"known\" population mean). The researcher arranged for eight randomly selected 7-year-old children to take instruction at this school and kept a careful record of how long it took each child. The times (in minutes) were 60, 120, 110, 80, 70, 90, 100, and 130. What should the researcher conclude? By answering the following questions, you carry out the appropriate test. Use 0.01 significance level. (a) Define the parameter of interest and state null and research hypotheses. (b) What is the comparison distribution based on above scenario? (c) What are the cut-off values for a test with significance level 0.01? (d) What is the observed t score? [Show workings] (e) Test your hypotheses and state your conclusions. (f) What is the effect size of the study? ANSWERS: 1. (a) Let denote.... Then we are testing: H0 : against H1 : X=swim time (in mins) X-Mx (X-Mx)2 = Mean of X= Mx Note: The comparison distribution is a distribution of the sample means, but the population variance is unknown and must be estimated from the sample Estimated population variance = Estimated standard deviation of the population = Variance of distribution of means = b) c) d) e) f) (X-Mx)2 Standard deviation of distribution of means =