Exam 14: Chi-Square Applications for Nominal Data

Six people have declared their intentions to run for a trustee seat in the next local election. A political poll is conducted during the campaign among 1,020 voters to determine if there is any clear preference among the voters. The responses are shown below. Determine the null and alternate hypotheses.

A student asked a statistics professor if grades were marked "on the curve." The professor decided to give the student a project to determine if last year's statistics grades were normally distributed. The professor told the student that last year's mean mark was 70 with a standard deviation of 10 and to use the following results. What is your decision if α = 0.05?

i. Nonparametric tests of hypotheses, which are also called distribution free tests, require the population to be normally distributed. Ii) The computed value of chi-square is always positive because the difference between the observed frequencies and the expected frequencies are squared. Iii) The shape of the chi-square distribution changes for each number of degrees of freedom.

Canadian Accounting classifies accounts receivable as "current", "late", and "not collectible". Industry figures show that 60% of A/R are current, 30% are late, and 10% are uncollectible. A law firm in Markham Ontario has 500 accounts receivable: 320 are current, 120 are late and 60 are not collectible. Are these numbers in agreement with the industry distribution?

i. There is not one, but a family of chi-square distributions. There is a chi-square distribution for 1 degree of freedom, another for 2 degrees of freedom, another for 3 degrees of freedom, and so on. ii. The shape of the chi-square distribution depends on the size of the sample. Iii) Small differences between observed and expected frequencies are due to chance.

Canadian Accounting classifies accounts receivable as "current", "late", and "not collectible". Industry figures show that 60% of A/R are current, 30% are late, and 10% are uncollectible. A law firm in Markham Ontario has 500 accounts receivable: 320 are current, 120 are late and 60 are not collectible. Are these numbers in agreement with the industry distribution? Using the data from this Megastat printout, you determine:

A survey of the opinions of property owners about a street widening project was taken to determine whether the resulting opinion was related to the distance of front footage. A randomly selected sample of 100 property owners was contacted and the results are shown below. What is the critical value at the 10% level of significance?

A question has these possible choices-excellent, very good, good, fair and unsatisfactory. How many degrees of freedom are there, using the goodness-of-fit test to the sample results?

i. The chi-square distribution with large degrees of freedom approaches a normal distribution. ii. The chi-square distribution is positively skewed. Iii) Nonparametric tests of hypotheses, which are also called distribution free tests, require the population to be normally distributed.

Which of the following is not a characteristic of the chi square distribution?

Six people have declared their intentions to run for a trustee seat in the next local election. A political poll is conducted during the campaign among 1,020 voters to determine if there is any clear preference among the voters. The responses are shown below. What is the critical value at the 5% level of significance?

At a recent automobile show, a sample of 135 people produced the following results. Use the 0.05 significance level to determine if there is a relationship between age and model preferred. Based on the analysis above, what can be concluded?

i. If the computed value of chi-square is less than the critical value, reject the null hypothesis at a predetermined level of significance. Ii) The alternative hypothesis states that there is a difference between the observed frequencies and the expected frequencies in a goodness-of-fit test. Iii) There are 2 degrees of freedom for a contingency table classifying three levels of income with each gender.