Example 6.2.1 In a chemical process the most important variables that are thought to affect the yield are pressure and temperature. Three levels of each factor are selected and a factorial erperiment in a CRD with two replications was performed. The results are as shown in table 6.2.1. Analyse the data and draw conclusions. Pressure Temperature 215 230 235 30 80.4 80.7 80.2 80.2 80.6 80.4 40 80.1 80.5 79.9 80.3 80 6 80 1
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- You are asked to determine whether laptop brand A charges a higher premium for its laptops than brand B. You observe a sample of six laptops, their prices and brand. You observe a performance benchmark x for each of the laptops. Let (yi, xi) denote the price and performance of laptop i. Your data are: Obs. i=1 i = 2 i = 3 i = 4 i = 5 i = 6 Brand Price A $1000 A $1500 A B B B $2000 $1500 $2000 $2500 Performance 1 2 3 3 4 5 Draw a scatter plot of price vs. performance. Which brand produces more expensive laptops on average in the sample? Would you say this brand charges a higher premium? Explain by writing down an appropriate regression model, estimation results and an intepretation of your results. If you omit brand information from your regression and just regress price on performance, are you likely to over or under-estimate the association between performance and price? Explain by determining the likely sign of the omitted variables bias as in lecture and comparing it with the…5 and 6. The following data was collected from 1 bag of Hershey Kisses®. Each Kiss® was weighed in grams with the wrapper and recorded in the table below. Hershey claims that there are 368 grams of chocolate in one bag. Hershey Kiss Weights in Grams 4.76 4.72 4.74 4.55 4.91 4.74 4.78 4.71 4.80 4.78 4.78 4.75 4.79 4.82 4.91 4.83 4.68 4.74 4.70 4.80 4.70 4.76 4.70 4.83 4.93 4.74 4.84 4.82 4.76 4.77 4.72 4.78 4.83 4.75 4.74 4.68 4.84 4.71 4.71 4.76 4.66 4.78 4.73 4.74 4.92 4.77 4.80 4.79 4.86 4.64 4.78 4.70 4.75 4.78 4.76 4.83 4.66 4.77 4.83 4.78 4.69 4.81 4.68 4.78 4.88 4.72 4.85 4.85 4.81 4.74 4.80 4.82 4.84 4.70 4.85 4.70 4.81 4.72 4.79 4.73 4.61 Based on Hershey's® claim for 368 total net grams of chocolate in the bag, approximately how many Kisses® too many or too few are there? Assume that the Kisses® were weighed with the wrapper, each wrapper weighs 0.12 grams, and the net grams listed on the bag are for the chocolate only. Give some possible…Blood pressure: A blood pressure measurement consists of two numbers: the systolic pressure, which is the maximum pressure taken when the heart is contracting, and the diastolic pressure, which is the minimum pressure taken at the beginning of the heartbeat. Blood pressures were measured, in millimeters, for a sample of 6 adults. The following table presents the results. Systolic Diastolic 130 116 133 112 134 107 Part: 0 / 4 76 Part 1 of 4 70 91 Critical value(s): 75 Send data to Excel 87 The least-squares regression line y = b + b₁ x= 4.4261 +0.6058x and (x-x)² = 690.0000 are known for this data. Use the critical value method to test Ho: B₁ = 0 versus H₁ : ₁ > 0. Can you conclude that systolic blood pressure is useful in predicting diastolic blood pressure? Use the a= 0.05 level of significance. 71 Find the critical value(s). Round the answer to three decimal places. If there is more than one critical value, separate them with commas. X +0 S
- A scientist wants to develop a model to describe the relationship between the average daily temperature, x °C, and her household’s daily energy consumption, y kWh, in winter. A random sample of the average daily temperature and her household’s daily energy consumption are taken from 10 winter days and shown in the table. x -0.4 -0.2 0.3 0.8 1.1 1.4 1.8 2.1 2.5 2.6 y 28 30 26 25 26 27 26 24 22 21 You may use: Sy=255 Sxy=283.8 Syy= 64.5 Find a value for the product moment correlation coefficient r for this data Explain what the value of the product moment corelation tells you about the relationship between daily temperature and the household energy consumption.Lead Measurement. Laboratories A and B made multiple measurements on prepared wastewater effluent specimens to which lead (Pb) had been added in the amount of 1.25 µg/L or 2.5 µg/L. The background lead concentration was low, but not zero. Compare the bias and precision of the two laboratories. Laboratory A Spike = 1.25 1.1 2.0 1.3 1.0 1.1 0.8 0.8 0.9 0.8 Spike = 2.5 2.8 3.5 2.3 2.7 2.3 3.1 2.5 2.5 2.5 Laboratory B Spike = 1.25 2.35 2.86 2.70 2.56 2.88 2.04 2.78 2.16 2.43 Spike = 2.5 5.30 4.72 3.64 5.04 3.62 4.53 4.57 4.27 3.88of colour Example 13.7 A company has introduced a new drug B to cure common cold. It is being compared against an existing drug A. The relevant data are shown below: Нelped Harmed No effect Total Drug A Drug B 44 10 26 80 52 10 18 80 Total 96 20 44 160 Is the new drug more effective in curing cold?
- Q.1 Q.1 Two samples A and B were taken from a large concrete mix and tested for the compressive strength of concrete (in MPa), find the mean, median and mode of cach of the two samples. The results of tested specimens from each sample were as follows: 国 Compressive Strength 15 18 21 24 27 30 (MPa) Sample A Frequency 2 2 4 1 Sample B Frequency 3 2 2 1 Option 1 13Can you explain 4.31 ? Thank youA random sample of 42 earthquakes that have occurred between January 2015 and September 2017 was selected and for each earthquake the magnitude of the earthquake and the number of people killed was recorded. The data appear in the scatterplot below. 400 350 300 250 200 150 100 50 0 3 -50 4 5 6 7 8 9 10 -100 -150 Magnitude of Earthquake 8 Consider the scatterplot above question 2. Use this scatterplot to describe completely the relationship between the magnitude of the earthquake and the number of people killed. Positive and linear Negative, moderate, linear O Negative, strong, linear Positive, moderate, linear Number of People Killed ---
- Q3.1 Cholesterol Before and After Treatment A random sample of 16 people with high cholesterol were given a new drug designed to lower cholesterol levels. The table contains the cholesterol levels (in milligrams per deciliter) measured before and after treatment for each person. Person 1 2 3 4 Before 237 248 260 266 After 176 178 191 192 Person 9 10 11 14 15 16 Before 283 284 286 289 292 293 295 299 After 215 212 204 214 214 192 216 206 Save Answer Do these data support the claim that the average reduction in cholesterol for people on this medication would be greater than 70 mm/dL? Q3.2 Conditions Hypotheses: Write the appropriate hypotheses, including defining the parameters and identifying the subscripts appropriately. (Note: you are not required to use Greek letters. For example, writing sigma is sufficient for σ.) Save Answer 5 6 7 273 274 275 277 195 187 212 196 12 Q3.3 Mechanics Conditions: Use your own paper to explain how the Normal condition for this test has been met. Then…Question 4 Beachcomber Ltd in a local car dealership that sells used and new vehicles. The manager of the company wants to know how different variables affect the sales of his vehicles. A random sample of yearly data was taken with the view to testing the model: SALES=a+BAGE+YMIL+&ENG Where SÄLES= amount that a vehícle is sold for($000's), AGE = age of the vehicle, MIL= the total mileage of the vehicle at the point of sale and ENG= the size of the engine. The sample of data was processed using MINITAB and the following is an extract of the output obtained: The regression equation is ***** Coef StDev t-ratio p-value Predict or Constan 1.7586 0.2525 6.9648 0.0000 AGE 0.2124 0.3175 0.5042 ** MIL -0.7527 0.3586 -2.0991 7.7664 0.0000 *** ENG 4.8124 Analysis of Variance DF MS Source 3 413.1291 138.709 **** 0.00 Regressi 7 on 50 457.7607 2.2888 Error Total 53 a) What is dependent and independent variables? b) Fully write out the regression equation c) Fill in the missing values *', '**',…QUESTION 14 CardioGood Fitness Treadmill Products Data The market research team at CardioGood Fitness retail store wants to investigate whether there are differences across the product lines of treadmills sold; TM195 (low-end model), TM498 (medium grade model) and TM798 (high-end model) with respect to customer characteristics. The team decides to collect data on individuals who purchased a treadmill at a CardioGood Fitness retail store during the past three months. One question the team is interested in is if there is a difference in the miles of intended use of the treadmill between males and Females. t-Test: Two-Sample Assuming Unequal Variances MaleMiles Female Miles Mean 112.81 89.99 Variance 2991.43 2006.76 Observations 104 76 Hypothesized Mean Difference df 176 t Stat 3.0732 P(T<=t) one-tail 0.0012 t Critical one-tail 1.6536 P(T<=t) two-tail 0.0025 t Critical two-tail 1.9735 In the essay box, clearly answer questions 1-5 below: 1. Is this conducting a one-sided test or a…