Construct a 5% confidence interval for the ratio of two population variances for prices Playing video games of the two portfolios. Explain if the interval constructed is consistent with the (hours) GPA assumption of variances that was stated in (i) above. 1 .95 (6 marks) 7 3.65 i) Using the 95% confidence interval for the mean difference in the output above, can 5 3.55 you conclude a difference in prices between the two portfolios? Justify your answer. 3 3.58 10 2.98 (2 market 17 1.75 15 2.50 The manufacturer of fuel additive claims that the use of this additive increased mileage. 9 2.20 A random sample of six cars was selected and these cars were driven for one week without 3.0 the fuel additive and then for one week with the fuel additive. The Minitab output below 13 2.90 gives the paired T-Test and et for these cars without and with the additive. Assume the distance travelled with or without the additive are normally distributed. The data collected were analysed and the output is shown below. Paired T-Test and Cl: Without, With Regression Analysis: GPA versus Time playing (hours) Paired T for Without - With Analysis of Variance SE Mean Source DF Adj ss Adj MS s F-Value P-Value Without 23.40 5.42 2.21 Regression 1 3.202 3.2024 20.93 0.002 With 6 25.22 5.79 2.36 Time playing (hours) 3.202 3.2024 20.93 0.002 wefence 6 1 D 1. 423 0.581 Error 1 . 224 0. 1530 Total 4. 426 T-Test of mean difference - 0: T-wake - Model Summary Assume that the population distributions are approximately normally distributed_anews the questions below. S R-8q R-sq(adj) R-sq (pred) 0. 391165 68.89% 60. 84% i) Find the missing values of D and T Goutput. Coefficients (3 marks) Term Coef SE Coef T-Value P-Value VIF i) Is there enough evidence at 5% significance level to conclude whether the use of fuel Constant 0.248 16.08 0.000 additive increases the mean mileage of cars? Time playing (hours) M 0. 0250 -4.57 0. 002 1.00 (5 marks) Assume that both the variables are normally distributed, answer the following questions. Leave QUESTION 5 all calculated values to 4 decimal places. An instructor wants to know if there is a relationship between playing video games and a) Using the data given, compute using formula the value of Pearson Product Moment students' academic performance in her class. Ten students' weekly hours spent playing video Correlation Coefficient. Hence, explain its meaning. games and grade point averages (GPAs) were collected. The results are shown in the table (5 marks) below. b) Find the regression equation line using the least squares method (indicating the dependent and independent variable clearly in context of the problem) and interpret the value of the slope. (6 marks)KEY FORMULAS c) Is it meaningful to interpret the value of C? Justify your answer. (2 marks) Binomial probability formula P(X = x)=$ 0*(1-py *; x=0,12. ....n d) Determine the value of W given in the output and interpret its value. (3 marks) Poisson probability formula P(X = x)=* *" x! -; x =0,1, 2, ... e) Test whether the linear regression model is significant at 1% significance level. (4 marks) CONFIDENCE INTERVALS Parameter & description Two-sided (1 - a)100% confidence interval END OF QUESTION PAPER Mean, u, variance, oz unknown, small samples of = n-1 Difference in means, #1 -H2 , variances of =027 and unknown PVn nz of = 1, + n2 - 2 , Sp = (n - 1) s,7 + (n2 - 1) $2 My + 12 -2 Difference in means, My - H2. variances of # 62 and unknown df = (s,?, + s?2 P n, -1 n2 -1 Mean difference for paired samples, up of =n-1 where n is no. of pairs Variance, oz (n-1)s2 (n-1)s' f =n-1 Ratio of the variances of?/622 $1 Fa/ 2 : 42 141: V1 = n -1, v2 = 02 -1