Recent revenue shortfalls in a southern state led to a reduction in the state budget for higher education. To offset the reduction, the largest state university proposed a 25% tuition increase. It was determined that such an increase was needed to simply compensate for the lost support from the state. Random samples of 50 freshmen, 50 sophomores, 50 juniors, and 50 seniors from the university were asked whether they were strongly opposed to the increase, given that it was the minimum increase necessary to maintain the university's budget at current levels. The results are given in the following table.

To compare the four classes (year in school) with respect to their opinion regarding the proposed tuition increase, which distribution should we calculate?

In the United States, there is a strong relationship between smoking and education, with well-educated people less likely to smoke. A study in France included a sample of 459 individuals who were selected at random from those who had visited a health centre for a routine checkup. Education is classified into three categories corresponding to the highest level of education and smoking status is classified into four categories.

Select which statements below are true or false.

The following table describes the opinions of the 570 people that returned the questionnaire in the survey described above (questions 1–3). Students were classified by class (freshman, sophomore, junior, or senior), and by their opinion of campus residence quality (high quality, medium quality, low quality).

A survey of undergraduate college students at a small university was recently done by an administrator in charge of residential life services. A random sample of 300 students was selected from each class level (freshman, sophomore, junior, senior). Each student was asked to complete and return a short questionnaire on the quality of campus residence (high quality, medium quality, low quality). Some students returned the questionnaire, and some didn't. Of those who did return the questionnaire, the results are summarised in the table below:

An inspector inspects large truckloads of potatoes to determine the proportion p in the shipment with major defects prior to using the potatoes to make potato chips. Unless there is clear evidence that this proportion, p, is less than 0.10, he will reject the shipment. He will test the hypotheses

H0: p = 0.10, Ha: p < 0.10.

The inspector selects an SRS of 100 potatoes from over 2000 potatoes on the truck. Suppose that six of the potatoes sampled are found to have major defects.

According to the National Institute on Alcohol Abuse and Alcoholism (NIAAA), 41% of college students nationwide engage in “binge drinking” behaviour, having five or more drinks in one occasion during the past two weeks. A college president wonders if the proportion of students enrolled at the college that binge drink is actually lower than the national proportion. In a commissioned study, 348 students are selected randomly from a list of all students enrolled at the college. Of these, 132 admitted to having engaged in binge drinking.

With a P-value > 0.10, which of the following conclusions is reasonable?

In 1965, about 44% of the Australian adult population had never smoked cigarettes. A national health survey of 1205 Australian adults (presumably selected randomly) during 2006 revealed that 615 had never smoked cigarettes.

The P-value of a two sided test of significance against a null value of 0.44 is

A noted psychic was tested for ESP. The psychic was presented with 400 cards face down and asked to determine if each of the cards was one of four symbols: a star, cross, circle, or square. The psychic was correct in 120 cases. Let p represent the probability that the psychic correctly identifies the symbols on the cards in a random trial. Suppose you wish to see if there is evidence that the psychic was doing better than just guessing.

To make this determination you test the hypotheses H0: p = 0.25 versus Ha: p > 0.25. The P-value of your test is:

In 1965, about 44% of the Australian adult population had never smoked cigarettes. A national health survey of 1205 Australian adults (presumably selected randomly) during 2006 revealed that 615 had never smoked cigarettes.

Suppose you wished to test whether there has been a change since 1965 in the proportion of Australian adults that have never smoked cigarettes. Which of the following are the appropriate hypotheses?