ECON2027: Intermediate Statistics Graded Worksheet (40%) Due date: March 15th 2024 at 11:55 pm EC/10:55 pm Jam Instructions: Answer the following questions and submit your responses to the relevant assignment dropbox on the course page. Question 1 PETROGAS is testing new filters for its motorbikes. One brand of filter (Filter A) is placed in one motorbike, and the other brand (Filter B) is placed in the second motorbike. Random samples of air released from the motorbikes are taken at different times throughout the day. Pollutant concentrations are measured for both motorbikes at the same time. The following data represent the pollutant concentrations (in parts per million) for samples taken at 20 different times after passing through the filters. a. Test the hypothesis that the mean for the pollutant concentration for Filter B is greater than 30. Use the 1% level of significance. [5 marks] b. Construct a 95% confidence interval for the difference in mean pollutant concentration, where a difference is equal to the pollutant concentration passing through Filter A minus the passing through Filter B. [5 marks] c. Using the 5% significance level, determine whether there is evidence that mean for the pollutant concentration for Filter A exceeds Filter B [5 marks] d. Confirm test results in part (c) using JASP. Note: All JASP input files and output tables should be provided [2 marks] Question 2 The data below shows the LSAT scores of 30 students at Georgetown University in Massachusetts. 1561 1554 1536 1531 1523 1518 1515 1511 1506 1500 1499 1493 1490 1489 1485 1482 1482 1479 1477 1466 1453 1448 1439 1432 1423 1421 1413 1407 1394 1388 a. Calculate the interquartile range for the LSAT scores[2 marks] b. Test the hypothesis that mean is greater than 1500. Use the 1% level of significance. [5 marks] c. Would your conlcusion change at the 10% level of significance? Show all steps for the hypothesis test [5 marks] d. Confirm test results in part (b) using JASP. Note: All JASP input files and output tables should be provided [2 marks] Question 3 A 2020 poll in Bahamas surveyed 2,400 people about taxing sweetened beverages. The results are provided in the table below and are classified by age group and opinion: a. State both the null and alternative hypotheses. [2 marks] b. Provide the decision rule for making this decision. Use an alpha level of 5%. [2 marks] c. Show all of the work necessary to calculate the appropriate statistic. [5 marks] d. What conclusion are you allowed to draw? [2 marks] e. Would your conclusion change at the 10% level of significance? [2 marks] f. Confirm test results in part (c) using JASP. Note: All JASP input files and output tables should be provided [2 marks] Question 4 Bad Dawgz is hosting its annual hot dog eating competition which involves eating 14 hot dogs, six inches in length. The following data represent the times (in seconds) taken by each contestant to eat the first hot dog and the fourteenth (last) hot dog. Twelve contestants finished all 14 hot dogs. a. Calculate a 90% confidence interval for the mean time taken by each contestant to eat the (i) first hot dog and (ii) last hot dog. [4 marks] b. Test the hypothesis that the difference between the two mean times for both is 35 seconds. Use the 5% level of significance. [5 marks] c. Subsequently, it was learnt that the times for the last hot dog were incorrecly recorded and that each of the values is 10 seconds too large. What, if any, difference does this make to the results of the test done in part (b)? Show all steps for the hypothesis test [5 marks] TOTAL: 60 MARKS