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 = QUESTION: An organizational specialist is hired as a consultant to a company planning to open a coffee house for college students. The company wants to know if the customers will drink more coffee if the coffee house is decorated in a Paris motif or in a San Francisco motif. To test this, the researcher sets up two similar rooms, but with the two different motifs. She then arranges to have eight students spend an afternoon in each room while being allowed to drink all the coffee they like. (The order in which they sit in the rooms is rotated, so that half do their first afternoon in the Paris room and half in the San Francisco room.) The amount each student drinks is recorded below: Cups of Coffee Consumed for each Motif Participant Paris San Francisco Participa nt A 8.5 San Francisco 8.4 B 4.3 4.6 C 2.0 1.7 D 7.8 7.3 E 7.0 7.2 F 9.1 7.4 G 3.3 3.0 H 3.5 3.5 Paris Is there a significant difference between the numbers of cups of coffee consumed in the two rooms? (a) Define parameter of interest and state null and research hypotheses. (b) What is the comparison distribution based on above scenario? (b)What are the cut-off values for a test with significance level 0.05? (c) What is the observed t score? [Show workings] (d)Test your hypotheses and state your conclusions. (f) What is the effect size of the study? ANSWER SHEET (a) Let d be Then our hypotheses are: null hypothesis: H0 : d, research hypothesis: H1 : d (b) Paris San Francisco Xd = XS.F. XParis Xd -Mx (Xd -Mx)2 The mean difference score = The mean of the population of difference scores is: The difference scores are: The mean difference score: The estimated variance of the population of difference scores is: The estimated standard deviation of the population of difference scores is = The variance of the distribution of means : The Standard deviation of distribution of means: SD X =S M = Therefore the characteristics of comparison distribution is: (c) (d) (e) (f)