Q8. X is a normally distributed random variable with unknown µ and a known variance, o. X and s' are the unbiased, sample mean and sample variance estimates of u and o respectively calculated from a small random sample. The 95% C.I. is calculated as: A. X±Zo.025. B. µ±Zo.025. n s2 C. X±Zo.025. s2 D. μ+ Ζo.025.

10.2.3 WP GO Tutorial The diameter of steel rods manufactured on two different extrusion machines is being investigated. Two random samples of sizes n₁ = 15 and n₂ = 17 are selected, and the sample means and sample variances are x₁ = 8.73, ² 0.35,₂ = 8.68, and s² = 0.40, respectively. Assume that o and that the data are drawn from a normal distribution. - = 0 a. Is there evidence to support the claim that the two machines produce rods with different mean diameters? Use α = 0.05 in arriving at this conclusion. Find the P-value. b. Construct a 95% confidence interval for the difference in mean rod diameter. Interpret this interval.

Consider a random sample of size n from a normal distribution with unknown mean u and unknown variance o?. Suppose the sample mean is X and the sample variance is S?. n = 16, the observed sample mean i is 8.9. the observed sample variance s? is 25 and 4o : 10.5. Suppose we now want to test Ho : o? = of versus H1 : o? + of. Which of these test statistics should we use? Select one: (n-1)s? W = of a. O b. Z %3D O c. T= S/n Let o = 36. What is the (appropriate) observed test statistic? Give answer to three decimal places. What is the p-value of the (appropriate) observed test statistic for testing Ho : o? = of versus H1 : o? + of you just computed? Give answer to three decimal places.

Consider a random sample of size n from a normal distribution with unknown mean u and unknown variance o?. Suppose the sample mean is X and the sample variance is S?. n = 16, the observed sample mean i is 8.9. the observed sample variance s is 25 and µo = 10.5. Suppose we now want to test Ho : o² = of versus H1 : o? + of. Which of these test statistics should we use? Select one: O a. W = (n-1)s O b. Z X-P O c. T = S/n Let of = 36. What is the (appropriate) observed test statistic? Give answer to three decimal places.