Exam 17: Additional Tests for Nominal Data: Chi-Squared Tests

A psychologist claims that people who exercise regularly are more content with their body image. A random sample of 102 people was taken, where they were asked if they regularly exercise and if they were content with their body image. Not content Content Exercised regularly 20 30 Did not exercise regularly 28 24 Is there significant evidence to support this claim? Test at the 1% significance level.

A left-tailed area in the chi-squared distribution equals 0.975. For df = 11, the table value equals:

An Australian tyre manufacturer operates a plant in Melbourne and another plant in Adelaide. Employees at each plant have been evenly divided among three issues (wages, working conditions and super benefits) in terms of which one they feel should be the primary issue in the upcoming contract negotiations. The secretary of the union has recently circulated pamphlets among the employees, attempting to convince them that super benefits should be the primary issue. A subsequent survey revealed the following breakdown of the employees according to the plant at which they worked and the issue that they felt should be supported as the primary one. $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Issues }$ Plant Location Very interesting Fairly interesting Not interesting Melbourne 60 62 78 Adelaide 70 56 74 Can you infer at the 5% significance level that the proportional support by the Melbourne employees for the three issues has changed since the pamphlet was circulated?

Which of the following uses a contingency table?

In a goodness-of-fit test, the null hypothesis states that the data came from a normally distributed population. The researcher estimated the population mean and population standard deviation from a sample of 200 observations. In addition, the researcher used 5 standardised intervals to test for normality. Using a 10% level of significance, the critical value for this test is 4.60517.

Which of the following statements is not correct?

Which of the following statements is true for the chi-squared tests?

Whenever the expected frequency of a cell is less than 5, we must increase the significance level.

A chi-squared goodness-of-fit test can be conducted either as a two-tail test or as a one-tail test.

In a chi-squared test of independence, the value of the test statistic was $x ^ { 2 } =$ 15.652, and the critical value at $\alpha = 0.025$ was 11.1433. Thus we must reject the null hypothesis at $\alpha = 0.025$ .

In a number of universities in Australia, lecture recordings online are provided to all students. There is growing concern amongst teaching staff that lecture recordings are used as a substitute for lecture attendance and that this is leading to a greater fail rate. At one particular university, a random sample of 224 students is taken, where the students are asked if they attended the majority of lectures for the last exam they took, or if they viewed the majority of lecture recordings online and then the student's records are followed up to see if the student passed that course. Attended lectures Viewed lecture recordings online Fail 40 80 Pass 56 48 Conduct a test to determine if enough evidence exists to infer that lecture attendance and passing a university course are related. Test at the 10% level of significance.

Suppose that a random sample of 150 observations was drawn from a population. After calculating the mean and standard deviation, each observation was standardised and the number of observations in each of the intervals below was counted. Can we infer at the 5% significance level that the data were drawn from a normal population? Intervals Frequency Z\leq-1.5 15 -1.51.5 13

For a chi-squared distributed random variable with 12 degrees of freedom and a level of significance of 0.05, the chi-squared value from the table is 21.0261. The computed value of the test statistics is 25.1687. This will lead us to reject the null hypothesis.

The number of degrees of freedom associated with the chi-squared test for normality is the number of intervals used minus the number of parameters estimated from the data.

Suppose that a random sample of 100 observations was drawn from a population. After calculating the mean and standard deviation, each observation was standardised and the number of observations in each of the intervals below was counted. Can we infer at the 10% significance level that the data were drawn from a normal population? Intervals Frequency Z\leq-1 12 -11 20

Consider a multinomial experiment involving n = 200 trials and k = 5 cells. The observed frequencies resulting from the experiment are shown in the following table. Cell 1 2 3 4 5 Frequency 4 11 14 12 9 The null hypothesis to be tested is as follows. $H_ { 0 } : p _ { 1 } = 0.10$ , $p _ { 2 } = 0.25$ $p _ { 3 } = 0.30$ $p _ { 4 } = 0.20$ $p _ { 5 } = 0.15$ $p _ { 5 } = 0.15$ .

Which of the following best describes the sampling distribution of the test statistic for a goodness-of-fit test with k categories?

The vice-chancellor of a university collected data from students concerning the building of a new library, and classified the responses into different categories (strongly agree, agree, undecided, disagree, strongly disagree) and according to whether the student was male or female. Which of the following tests should be used to test whether responses and gender are independent?

Which of the following best describes the approach taken if the expected frequency $e _ { i }$ for any cell i is less than 5?

The middle 0.95 portion of the chi-squared distribution with 9 degrees of freedom has table values of 3.32511 and 16.9190, respectively.