A researcher used Chi² for Goodness of Fit to evaluate if there is a difference in preferences for seasons (i.e., summer, fall, winter or spring), in a sample of n = 90 participants. If the computed Chi² = 12.56, what is the correct statistical decision for the outcome of this test?

Group of answer choices

reject H₀ with either, p < .05 or p < .01.

reject H₀ with p < .05 but fail to reject with p < .01.

reject H₀ with p < .01 but fail to reject with p < .05.

fail to reject H₀ with either p < .05 or p < .01.

A large value of the computed Chi² for Goodness of Fit test indicates that ______________.

Group of answer choices

the distribution of frequencies in the sample differs from the distribution of frequencies in the population predicted by the null hypothesis.

the distribution of frequencies in the sample is similar to the distribution of frequencies in the population predicted by the null hypothesis.

Three months ago, a national survey showed that 40% of population approved the president's domestic policy, 50% disapproved, and 10% had no opinion. A researcher plans to use a sample of n = 500 people to determine whether public opinions have changed during the past three months. If a Chi² for Goodness of Fit is used to evaluate the data, what is the expected frequency f_e for the Approved category?

Group of answer choices

What is the degree of freedom, df of Chi² for Independence if one nominal variable consists of 4 categories and the second nominal variable consisted of 3 categories?

A researcher selected a sample of 100 adults to investigate a relationship between gender (male/female) and a person's voting registration status (i.e., Registered to Vote/Not Registered to Vote). Each participant was asked if he/she is registered to vote in the upcoming presidential election. The collected data are presented in the table below. If the Chi² for Independence is used for statistical analysis, what is the expected frequency, f_efor the Females who are Not Registered to Vote category?

	REGISTERED to VOTE	NOT REGISTERED to VOTE
MALE	40	20
FEMALE	30	10