Question

8. Suppose you poll 800 people on an upcoming referendum and 425 of them say they are going to vote yes. Perform a one-sided significance test of the hypothesis that 50% of the voters will vote yes against an appropriate alternative. How sure can you be that the referendum is going to pass?
A. ≈ .0192 B. ≈ .0384 C. ≈ .9616 D. ≈ .9808 E. other value
9. If a simple random sample of 35 tires yields an average lifetime x¯ = 59,700 miles and a sample standard deviation of s = 1,000 miles, perform an appropriate one-sided significance test of the company’s claim that the average lifetime of the tires is 60,000 against an appropriate alternative. How sure can you be based on the sample that the company’s claim is false?
A. ≈ .9808 B. ≈ .9616 C. ≈ .0384 D. ≈ .0192 E. other value
10. Define a pivotal quantity.

Answer 1

8) Required value is nothing but the p-value of the test

  > x <- 425 > n <- 800 > p <- x/n > p0 <- 0.5 > test <- prop.test(x,n,p=p0,alternative="greater") > > # Reject H0 > 1-test$p.value [1] 0.9583998 > 

E. Other value (value = 0.9584)

9)

  n <- 35 > x_bar <- 59700 > s <- 1000 > mu0 <- 60000 > t <- (x_bar-mu0)*sqrt(n)/s > t [1] -1.774824 > critical <- qt(0.05,n-1) > critical [1] -1.690924 > p_value <- 1-pt(t,n-1);p_value [1] 0.9575593

E .Other value (value = 0.9576)

10)

Definition: Pivotal quantity: a pivotal quantity or pivot is a function of observations and unobservable parameters such that the function's probability distribution does not depend on the unknown parameters.

Hope this helps!