Question

10) In a left-tailed test comparing two means with unknown variances assumed to be equal, the test statistic was t = -1.81 with sample sizes of n₁ = 8 and n₂ = 12. The p-value would be:

Select one:

a. between .025 and .05

b.between .01 and .025

c.between .05 and .10

d. Must know α to answer

The owner of a fish market determined that the weights of catfish are normally distributed, with a mean of 3.2 pounds and a standard deviation of 0.8 pound.

a)     What is the probability that a randomly selected catfish will weigh less than 2.2 pounds?

b) What is the probability that a randomly selected catfish will weigh more than 4.4 pounds?

c) What is the probability that a randomly selected catfish will weigh between 3 and 5 pounds?

d) A citation catfish should be one of the top 2% in weight. At what weight (in pounds) should the citation designation be established?

e) A random sample of 64 fish is selected. What is the probability that the sample mean will be less than 3.5 pounds?

f) If random samples of 64 fish are selected, 90% of the sample means will be greater than what value?

Answer 1

10. n_1 = 8 n_2 = 12 d.f = n_1 + n_2 - 2 = 18 t = - 1.81 Fo left tailed t - test p-value = p [t df less than t] = p[t_18 less than - 1.81] = 0.0435 between 0.025 & 0.05 * given that X: weight of cat fish X sim Normal (mu = 3.2, sigma = 0.8) (a) p(x less than 2.2) = p(z less than 2.2 - 3.2/0.8] = p(z less than -1.25] = 0.1056 b) p(x greater than 4.4) = p[z greater than 4.4 - 3.2/0.8] = p[z greater than 1.5] = 0.0668 C) p(x less than x less than 5) = p[3 - 3.2/0.8 less than z less than 5 - 3.2/0.8] = p[- 0.25 less than z less than 2.25] = 0.5865 d) We want x_0 such that p[x greater than x_0] = 0.02 p[z greater than x_0 - 3.2/0.8] = 0.02 Using Normal probability table x_0 - 3.2/0.8 = 2.054 = > x_0 = 4.8432 e. Let n = 64 sample mean = x bar Using Central limit theorem x bar Normal (mu, sigma/ squareroot n) p[x bar less than 3.5] = p[z less than 3.5 - 3.2/0.8/ squareroot 64 = p[z less than 3] = 0.9987 f) we want x, such that p[x bat greater than x_1] = 0.9 p[z greater than x_1 - 3.2/0.8/ squareroot 64 = - 1.282 = > x_1 = 3.0718 pounds