Statistics and Probability Answers

Use the traditional method in testing the hypothesis in the problems below. In each problem, state the following:

a. State the hypotheses and identify the claim.

b. Find the critical value(s)

c. Find the test value

d. Make the decision

e. Summarize the result

1. The mean Verbal SAT score for the population of first year students at Radford is 520. The standard deviation of scores in this population is 95. An investigator believes that the mean Verbal SAT of first year psychology majors is significantly different from the mean score of the population. The mean of a sample of 36 first year psychology majors is 548. Test the investigator’s prediction using an alpha level of 0.05.

We want to estimate the mean of a population. A random sample of subjects is selected and the sample mean is computed. What is the probability that the sample mean is within 3 units of the true mean if the standard error is 1.8?

Find the critical value (or values) for the 𝑡-test for each.

a. 𝑛 = 10 ; ∝= 0.05 ; right tailed

b. 𝑛 = 18 ; ∝= 0.10 ; two-tailed

c. 𝑛 = 6 ; ∝= 0.01 ; left-tailed

d. 𝑛 = 9 ; ∝= 0.025 ; right tailed

e. 𝑛 = 15 ; ∝= 0.05 ; two-tailed 

Leo a working student from STEM, rides a bicycle from house to school to save money. If the mean life of a tire is 10,000 km and the standard deviation is 200 km. 68% of all tires will have a life between how many kilometers?

A company makes electronic gadgets. One out of every 50 gadgets is faulty, but the company doesn't know which ones are faulty until a buyer complains. Suppose the company makes a Php 1,000.00 profit on the sale of any working gadget, but suffers a loss of Php 25, 000.00 for every faulty gadget because they have to repair the unit.

 The test scores of 40 students are summarized in the frequency distribution below. Find the standard deviation. Score Students 50-59 5 60-69 8 70-79 6 80-89 13 90-99 8