STA215 · TU past paper
Statistics II 2075 question paper
The complete TU 2075 exam paper for Statistics II (STA215), all 12 questions with solved model answers written to the mark scheme.
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- 110 marksNumericalIntroduction of multiple linear regressionHideAnswer
From the following information of variables X₁, X₂, and Y:
- $\Sigma X_1 = 272$
- $\Sigma X_2 = 441$
- $\Sigma Y = 147$
- $\Sigma X_1^2 = 7428$
- $\Sigma X_2^2 = 19461$
- $\Sigma Y^2 = 2173$
- $\Sigma X_1 Y = 4013$
- $\Sigma X_1 X_2 = 12005$
- $\Sigma X_2 Y = 6485$
- $n = 10$
Fit a regression equation Y on X₁ and X₂. Interpret the regression coefficients. [10]
Multiple Linear Regression (MLR) is a statistical technique that models the relationship between one dependent variable and two or more independent variables. It allows us to estimate/predict the dependent variable using several predicto...
- 210 marksNumericalLatin Square DesignHideAnswer
Latin Square Design
A Latin Square Design (LSD) is an experimental design used when experimental material is non-homogeneous in two directions (rows and columns). Local control is applied in both directions to reduce experimental error. The design is arrang...
- 310 marksNumericaltest for difference between two means and HideAnswer
What do you mean by hypothesis? Describe null and alternative hypothesis. A company claims that its light bulbs are superior to those of the competitor on the basis of study which showed that a sample of 40 of its bulbs had an average life time 628 hours of continuous use with a standard deviation of 27 hours. While sample of 30 bulbs made by the competitor had an average life time 619 hours of continuous use with a standard deviation of 25 hours. Test at 5% level of significance, whether this claim is justified.[10]
A hypothesis is a tentative statement or assumption about a population parameter (mean, proportion, variance, etc.) that is subject to verification using sample data through statistical testing. The null hypothesis is a statement of "no ...
- 45 marksNumericalTest of significance of regressionHideAnswer
Suppose we are given following information with n=7, multiple regression model is $\hat{A} = 8.15 + 0.6 X_1 + 0.54 X_2$. Here, Total sum of square = 1493, and Sum of square due to error = 91. Find i) $R^2$ and interpret it. ii) Test the overall significance of model [5]
- Sample size: $n = 7$ - Model: $\hat{A} = 8.15 + 0.6X1 + 0.54X2$ - Number of independent variables: $k = 2$ - Total Sum of Squares: $SST = 1493$ - Sum of Squares due to Error: $SSE = 91$ --- Sum of Squares due to Regression: $$SSR = SST...
- 55 marksNumericalTwo independent sample testHideAnswer
Chi-Square Test for Independence
The following data related to the number of children classified according to the type of feeding and nature of teeth. Do the information provide sufficient evidence to conclude that type of feeding and nature of teeth are dependent? Use chi square test at 5% level of significance.
$$\begin{array}{|c|c|c|} \hline \text{Type of feed} & \text{Normal} & \text{Defective} \ \hline \text{Breast} & 18 & 12 \ \text{Bottle} & 2 & 13 \ \hline \end{array}$$
[5]
Type of Feed Normal Defective Row Total ------------ Breast 18 12 30 Bottle 2 13 15 Column Total 20 25 N = 45 --- - $H0$: Type of feeding and nature of teeth are independent. - $H1$: Type of feeding and nature of teeth are dependent. -
- 65 marksNumericalDetermination of sample sizeHideAnswer
Determine the minimum sample size required so that the sample estimate lies within 10% of the true value 95% level of confidence, when coefficient of variation is 60% [5]
Parameter Value ------------------ Allowable relative error, $e$ 10% of true value = 0.10 Confidence level 95% Coefficient of variation, $CV$ 60% = 0.60 Formula For estimating the mean within a relative error $e$ (fraction of the true me...
- 75 marksNumericalEstimationHideAnswer
A manufacturer of computer paper has a production process that operates continuously throughout an entire production shift. The paper is expected to have an average length of 11 inches and standard deviation is known to be 0.01 inch. Suppose random sample of 100 sheets is selected and the average paper length is found to be 10.68 inches. Set up 95% and 90% confidence interval estimate of the population average paper length. [5]
Parameter Value ------------------ Expected/target mean 11 inches (target, not used in CI) Population standard deviation ($\sigma$) 0.01 inch Sample size ($n$) 100 Sample mean ($\bar{X}$) 10.68 inches Since $\sigma$ is known and
- 85 marksNumericalKruskal Wallis testHideAnswer
Kruskal-Wallis H Test for Catalyst Comparison
A chemist uses three catalysts for distilling alcohol and the results were tabulated below. Are there any significant differences between catalysts? Test at 5% level of significance. Use Kruskal-Wallis H test.
Catalyst Alcohol (in cc) C1 380 430 410 C2 290 350 270 250 270 C3 400 380 450 [5]
Catalyst Alcohol yield (cc) Sample size ------------------------------------------- C1 380, 430, 410 $n1 = 3$ C2 290, 350, 270, 250, 270 $n2 = 5$ C3 400, 380, 450 $n3 = 3$ Total: $N = 3 + 5 + 3 = 11$, significance level $\alpha = 0.05$. ...
- 95 marksNumericalLatin Square DesignHideAnswer
ANOVA Table Completion and Analysis
Source SS df MSS F --------------- Column 72 ? ? 2 Rows ? ? 36 ? Treatments 180 3 ? ? Error ? 6 12 Total ? ? Presence of Columns, Rows, Treatments, Error as sources indicates a Latin Square Design (LSD). --- Since the variation is partit...
- 105 marksQueuing systemHideAnswer
Define main component of queuing system. [5]
A queuing system is a system designed to perform certain tasks or process certain jobs by one or several servers, where jobs wait in a queue to be processed. The main components of a queuing system are described below: --- - This compone...
- 115 marksNumericalBernoulli single server queuing processHideAnswer
Jobs are sent to mainframe computer at a rate of 4 jobs per minute. Arrivals are modeled by a binomial process. a. Choose a frame size that makes the probability of a new received during each frame equal to 0.1. b. Using the chosen frame compute the probability of more than 4 jobs received during one minute. c. Compute mean and variance of inter arrival time? [5]
- Arrival rate: $\lambda = 4$ jobs per minute - Process type: Binomial (Bernoulli frames) - Target frame probability: $p = 0.1$ --- In a binomial process, arrivals occur one per frame with probability $p$, so the rate is: $$\lambda = \fr...
- 125 marksNeeds of applying non-parametric testsHideAnswer
Write short notes of the following: a. Need of non parametric statistical methods. b. Efficiency of Randomized Block Design relative to Completely Randomized Design [5]
--- Non-parametric statistical methods (also called distribution-free methods) are statistical tests that do not require assumptions about the population distribution from which the sample is drawn. The need for non-parametric methods ar...