MCQ

Question 1: There is a 5% chance that a randomly selected individual will have O-negative blood.Suppose we randomly select 15 individuals from the population and test them for O-negative blood. LetXdenote the number of individuals in the sample that have O-negative blood.

(a)What is the distribution ofXin conventional statistical notation?(2 marks)

• B(15, 0.05)
• B(15, 0.95)
• B(15, 7125)
• B(0.05, 15)
• N(15, 0.005)

(b)What is the probability that at least 2 individuals in the sample have O-negative blood?(2 marks)

• 0.9638
• 0.1710
• 0.0362
• 0.8290
• 0.0934

(c)What is the probability that less than 5 individuals in the sample have O-negative blood?(2 marks)

• 0.9999
• 0.3812
• 0.4633
• 0.9994
• 0.0006

(d)What is the P(1 < X4) equal to?(2 marks)

• 0.0356
• 0.5361
• 0.3896
• 0.1704
• 0.0678

(e)How many adults in the sample do we expect to have O-negative blood?(2 marks)

• 1
• 0.75
• 5
• 15
• 3

(f)What is the variance ofX?(2 marks)

• 1.9267
• 2
• 0.8441
• 15
• 0.7125

Question 2: Researchers examined the relationship between two quantitative variables, x and y. We aim to express the relationship between x and y by using the simple linear regression modelYi=0+ 1xi+ Ei.Use the information below to answer the following questions.

x = 696,y = 4498,xy = 177353,x2= 27194,y2= 1195676,n = 18

(a)What is the estimate of the slope coefficient 1?(2 marks)

• 9.6398
• 14.7005
• 12.6988
• 12.1643
• 9.4871

(b)What is the estimate of the intercept coefficient 0?(2 marks)

• 220.4641
• 402.3909
• 111.7256
• 278.7612
• 129.0179

(c)What is the value of the coefficient of determination?(2 marks)

• 0.6215
• 0.5822
• 0.6922
• 0.3906
• 0.9301

(d)Suppose we want to test, at the 5% level of significance, the null hypothesis H0: 1=2 vs the alternative hypothesis Ha:1<2. What is the value of the observed test statistic associated with this test?(2 marks)

• 5.1983
• 4.8932
• 4.7216
• 3.9453
• 5.4979

(e)What is the predicted value of ywhen x is equal to37?(2 marks)

• 229.6151
• 10.6982
• 318.2988
• 59.2131
• 90.7933

(f)What is the 99% prediction interval for y when x is equal to 42?(2 marks)

• (459.0487, 201.7211)
• (422.6652, 158.2080)
• (178.5487, 458.0538)
• (329.376,251.4971)
• (128.5554, 390.3297)