Question

(a) a study was performed to examine the personal goals of children in primary school. a random sample of students was selected from schools in ontario. the students received a questionnaire regarding achieving personal goals. they were asked what they would most like to do at school: make good grades, be good at sports, or be popular. each student's gender was also recorded. which hypotheses are being tested by the chi-square test?

A. The null hypothesis that boys are more likely than girls to desire good grades vs. the alternative that girls are more likely than boys to desire good grades.
B. The null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related.
C. The null hypothesis that the mean personal goal is the same for boys and girls vs. the alternative hypothesis that the means differ.
D. The null hypothesis that there is no relationship between personal goals and sex vs. the alternative hypothesis that there is a positive, linear relationship.
E. None of the above.
(b) The variables considered in a chi-squared test used to evaluate a contingency table
A. are normally distributed, can be averaged, are categorical.
B. have rounding errors.
C. have small standard deviations.
(c) A chi-squared statistic provides strong evidence in favor of the alternative hypothesis if its value is close to 0, a large negative number, or exactly a large positive number.

Answer 1

The chi-square test is used to determine if there is an association between two categorical variables and is typically right-tailed. The correct hypothesis for the study on personal goals is that sex and personal goals are not related. The chi-squared statistic provides strong evidence for the alternative hypothesis if it is a large positive number. Option B

Step-by-step explanation:

The question provided primarily deals with the concept of the chi-square test, a statistical method used to analyze categorical data. The main goal of a chi-square test is to determine if there is an association between two categorical variables. More specifically, in context:

For part (a), the correct hypothesis being tested by the chi-square test would be: B. The null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related.

In part (b), the variables considered in a chi-squared test used to evaluate a contingency table are categorical.

For part (c), a chi-squared statistic provides strong evidence in favor of the alternative hypothesis if it is a large positive number.

Whether examining the relationship between gender and personal goals or the fit of a sample distribution to a known distribution, the chi-square distribution is typically right-tailed and looks for differences that are larger than what would be expected if the null hypothesis were true. Option B