Eunice, a developmental psychologist, is investigating how styles of play differ for 3-year-old boys and girls. In her experiment, she brings each child into a room with three play stations set up. One station has a set of blocks, one has a collection of toy cars, and the third features a dollhouse. The child is told that he or she can play at one and only one station. His or her choice is recorded, the child is allowed to play for 15 minutes, and then he or she leaves and the next child is brought in. The children’s choices are below. Based on these data, is it possible to conclude that there is an association between gender and chosen toy? Test at a level of significance of 0.05.

Eunice, a developmental psychologist, is investigating how styles of play differ for 3-year-old boys and girls. In her experiment, she brings each child into a room with three play stations set up. One station has a set of blocks, one has a collection of toy cars, and the third features a dollhouse. The child is told that he or she can play at one and only one station. His or her choice is recorded, the child is allowed to play for 15 minutes, and then he or she leaves and the next child is brought in. The children’s choices are below. Based on these data, is it possible to conclude that there is an association between gender and chosen toy? Test at a level of significance of 0.05.

The U.S. Department of Agriculture (USDA) uses sample surveys to produce important economic estimates. One pilot study used samples of sales across the USA from two different months to estimate average wheat prices. Below are the summary statistics, in dollars per bushel, for these two months. Can we claim a difference between the mean prices in the two months?

a. Construct a suitable 95% confidence interval to determine if there is a difference between the mean prices in the two months. Give your full solutions. [4 marks]

b. With 95% confidence, can we claim a difference between the mean prices in the two months? Explain why. [1 mark]

c. Test at 5% if there is a difference between the mean prices in the two months. [9 marks]

d. Are the conclusions from the confidence interval and the significance test the same? Explain why or why not. [1 mark]

The U.S. Department of Agriculture (USDA) uses sample surveys to produce important economic estimates. One pilot study used samples of sales across the USA from two different months to estimate average wheat prices. Below are the summary statistics, in dollars per bushel, for these two months. Can we claim a difference between the mean prices in the two months?

a. Construct a suitable 95% confidence interval to determine if there is a difference between the mean prices in the two months. Give your full solutions. [4 marks]

b. With 95% confidence, can we claim a difference between the mean prices in the two months? Explain why. [1 mark]

c. Test at 5% if there is a difference between the mean prices in the two months. [9 marks]

d. Are the conclusions from the confidence interval and the significance test the same? Explain why or why not. [1 mark]

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.

Do women and men treat female and male children differently? An observational study was conducted near the primate exhibit at the Melbourne Zoo on weekends in 1997. The data are from 39 groups of three—one adult female, one adult male, and one toddler, in which the toddler was being carried. Recorded below is which adult (male or female) was carrying the toddler by the sex of the toddler.

A random sample of Victoria voters was asked about their use of the Internet and the type of community they lived in. The two-way table follows.

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.

Suppose we wish to test the null hypothesis that there is no association between education level and smoking status. Under the null hypothesis, the expected number of non-smokers with a primary school education is

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.

Which hypotheses are being tested by the chi-square test?

Which of the following statements is incorrect about the Chi-square distribution?