"COMPUTER ASSIGNMENTAUTUMN SESSIONSCHOOL OF COMPUTING, ENGINEERING &MATHEMATICS Student Family Name and ID numberGroup Member 1Group LeaderGroup Member 2 Group Member 2Group Member 3 Group Member 3Group Member 4 Group Member 4Unit Name:Statistics for BusinessUnit Number: Number of Questions: 6Value: 15%Total Number of Pages: 5Unit Coordinator: INSTRUCTIONS TO CANDIDATES(1) A file named “Assignment Data Sets”, containing the data sets for the followingquestions, can be downloaded from the e-learning site vUWS.You should findand download the data set your group has been allocated (eg data set 182).(2) You should use Excel to carry out all calculations and statistical analyses. To getstarted with Excel, see the instructions on page 13 of the textbook.(3) To complete this assignment, you must provide the Excel outputs for each of thequestions in a report.(4) Your assignment submitted must be typed and word-processed. (5) The maximum number of pages for each submission is six (6), not including thecover page. No mark will be given if the number of pages exceeds the limit. (6) The assignment is to be submitted in Week 13 in your tutorial class.(7) Any late assignments will be penalised 10% of the total mark per dayPage 1 of 6 A study was commissioned to investigate the characteristics of properties that are forsale. Data was collected on 60 houses and the following variables recorded.Column 1 ValueValue of house in thousands of dollarsColumn 2 Lot size Size of the property Column 3 BedNumber of bedrooms in house Column 4 BathNumber of bathrooms in houseColumn 5 RoomsTotal number of rooms in the houseColumn 6 AgeAge of house in yearsColumn 7 Fireplace Number of fireplacesQuestion 1 (1 + 1 + 1 + 1 = 5 marks)For the variable Value find thea) mean, b) median, c) range, d) standard deviation and e) coefficient of variation.Question 2 (4 marks)Estimate with 95% confidence the population average age of a house.Question 3 (5 marks)Using an appropriate hypothesis test, at a 5% level of significance, can you concludethat there is any difference between the average value between houses that have afireplace (Fireplace = 1) and houses that don’t have a fireplace (Fireplace = 0)?Question 4 (1 + 1 + 4 = 6 marks)(a) Estimate the regression equation to predict the Value (y) from the number ofRooms (x).(b) Determine the coefficient of determination and interpret its value.(c) Does the data provide evidence that the slope of the equation from part a) ispositive? Perform an appropriate hypothesis test using a 5% level of significance.NOTE:The data was randomly created for the sole purpose of this assignment.The data is normally distributed for all variablesPage 2 of 6 DATA SET: 1Question 1 (1 + 1 + 1 + 1 + 1 = 5 marks)Value($000) Mean 408.55 Standard Error 13.20 Median 404.10 Mode 246.40 Standard Deviation 102.24 Sample Variance 10452.81 Kurtosis 0.04 Skewness 0.52 Range 457.30 Minimum 229.40 Maximum 686.70 Sum 24513 Count 60 Mean = $408,550Median = $404,100 Range = $457,300 Standard Deviation = $102,239Coefficient of Variation = 25.02%Page 3 of 6 Question 2 (4 marks)Age Mean 19.833 Standard Error 0.966 Median 19 Mode 17 Standard Deviation 7.479 Sample Variance 55.938 Kurtosis -0.110 Skewness 0.333 Range 33 Minimum 7 Maximum 40 Sum 1190 Count 60 Confidence Level(95.0%) 1.932 The 95% confidence interval for the average age of a house is from 17.90 to 21.77 years old.Page 4 of 6 Question 3 (5 marks)Population 1 – Houses with a no fireplacePopulation 2 – House with a fireplace 1. H : µ = µ0 1 2H : µ ? µ A 1 2(x ? x ) ? ( ? ? ? ) 1 2 1 2 t ? ~ t 2.Assuming equal variancesn ?n ?2 1 2 2 2 ? (n ?1)s ? (n ?1)s ? ? 1 1 ? 1 1 2 2 ? ? ? ? ? ? ? ? ? (n ?n ? 2) n n ? 1 2 ? ? 1 2 ? 3. a = 0.05 t = 2.0020.025, 584. Reject H : if |t| > 2.002 0 5. t-Test: Two-Sample Assuming Equal Variances Variable 1 Variable 2 Mean 397.287 419.813 Variance 8773.672 12229.906 Observations 30 30 Pooled Variance 10501.789 Hypothesized Mean Difference 0 df 58 t Stat -0.851 P(T<=t) one-tail 0.199 t Critical one-tail 1.672 P(T<=t) two-tail 0.398 t Critical two-tail 2.002 |t| = 0.8516. Since 0.851 < 2.002 we cannot reject H0We cannot conclude that there is any difference between the average value between houses that have a fireplace (Fireplace = 1) and houses that don’t have a fireplace (Fireplace = 0). Page 5 of 6 "