A random sample of 40 business majors who had just completed introductory courses in both statistics and accounting was asked to rate each class in terms of level of interest on a scale of 1 (very uninteresting) to 10 (very interesting). The 40 differences in the pairs of ratings were calculated and the absolute differences ranked. The smaller of the rank sums, which was for those finding accounting the more interesting, was 281. Test the null hypothesis that the population of business majors would rate these courses equally against the alternative that the statistics course is viewed as the more interesting.

In Problem $29$, what is the probability that the product will last at least $1$ year? [Hint: Recall that the total area under the probability density function curve is $1$.]

Can a probability be greater than 1 ?

What is the probability of a homozygous recessive offspring?

Consider the previous exercise. In each case, interpret the term "probability" for the random phenomena. Explain why the term "probability" does not apply to those who are not at random.

Find the probability. Assume a number cube has six sides. What is the probability of a number cube coming up an even number three times in a row?

From an original deck of 26 alphabet cards, the X-card is missing. What is the probability of drawing A, E, I, O, or U from the deck? Express the probability as a decimal.

Suppose that the probability of a player hitting a home run is $\dfrac1{20}.\quad$ In 5 tries what is the probability that the player hits at least 1 home run?

The Gallup organization has asked opinions about suppor t of labor unions since its first poll in 1936, when 72 % of the American population approved of them. In its 2014 poll, it found that support of labor unions had fallen to 53% of Americans, based on a sample of 1,540 adults.

a. Calculate an estimated margin of error for these data.

b. What is the range of likely values for Americans who support labor unions in 2014?

c. This analysis is an example of

i. descriptive statistics

ii. inferential statistics

ill. a data file

iv. designing a study.

The sample space of the toss of a fair die is:

$$S=\{1,2,3,4,5,6\}$$

If the die is balanced each simple event has the same probability. Find the probability of the following events.

A batter is taking batting practice. The probability she hits a ball is 0.4, that she swings and misses is 0.3, that she does not swing is 0.25, and that she is hit by the ball is 0.05. Each swing is an independent event. a What is the probability that she hits the ball two times in a row? b What is the probability that she swings and misses three times in a row? c What is the probability she hits the ball, and then swings and misses two times in a row? d What is the probability that she does not swing twice in a row, and then gets hit by a ball?

Describe an experiment that has a probability of 1.

A Statistics professor has observed that for several years students score an average of 105 points out of 150 on the semester exam. A salesman suggests that he try a statistics software package that gets students more involved with computers, predicting that it will increase students' scores. The software is costly, and the salesman offers to let the professor use it for a semester to see if the scores on the final exam increase immensely. The professor will have to pay for the software only if he decides to continue using it.

c) In this context, explain what would happen if the professor makes a Type I error.

Interest centers around the nature of an oven purchased at a particular department store. It can be either a gas or an electric oven. Consider the decisions made by six distinct customers. (a) Suppose that the probability is 0.40 that at most two of these individuals purchase an electric oven. What is the probability that at least three purchase the electric oven? (b) Suppose it is known that the probability that all six purchase the electric oven is 0.007 while 0.104 is the probability that all six purchase the gas oven. What is the probability that at least one of each type is purchased?