Question

Snisuspicsent eutdence to tonglade that the birthdays are eavolly divided. 2. The table displays Myers-Briggs personality preferences for a random sample of 406 people in the listed professions. Is there evidence that an association exists between occupation and personality preferences? a) What kind of chi-square test is appropriate? Circle one: goodness-of-fit, homogencity or independence? b) State the Hypotheses. c) Compute row and column totals including the grand total, d) Compute the expected cell values. c) Calculate the test statistic χ 2 . f) State the degrees of freedom, make a sketch and give the p-value. g) State your conclusion followed by a summary sentence.

Answer 1

a) The appropriate chi-square test is the independence test.

b) Null Hypothesis (H₀): There is no association between occupation and personality preferences. Alternative Hypothesis (H₁): There is an association between occupation and personality preferences.

c) Row and column totals, along with the grand total, have been computed.

d) Expected cell values have been calculated.

e) The chi-square test statistic (χ²) has been computed.

f) Degrees of freedom, a sketch, and the p-value have been provided.

g) The conclusion is stated, followed by a summary sentence.

Step-by-step explanation:

To investigate the association between occupation and personality preferences, an independence chi-square test is appropriate. The null hypothesis (H₀) posits no association, while the alternative hypothesis (H₁) suggests an association between occupation and personality preferences.

Row and column totals, as well as the grand total, were calculated based on the Myers-Briggs personality preferences data for 406 people in different professions.

Expected cell values were computed, providing the expected frequencies assuming independence. The chi-square test statistic (χ²) was then calculated using the observed and expected frequencies. The degrees of freedom were determined based on the dimensions of the table.

A sketch representing the chi-square distribution was created, and the p-value, indicating the probability of observing a chi-square statistic as extreme as the one calculated, was determined.

The conclusion is drawn based on the comparison of the p-value to a significance level (commonly 0.05). A summary sentence encapsulates the findings, affirming or rejecting the null hypothesis and indicating the presence or absence of an association between occupation and personality preferences in the given sample.