Exam 15: Chi-Squared Tests

To analyze the relationship between two nominal variables,which test(s)can you use?

Consider a multinomial experiment involving 160 trials 4 categories (cells).The observed frequencies resulting from the experiment are shown in the accompanying table. Category 1 2 3 4 Frequency 53 35 30 42 Use the 10% significance level to test the hypotheses: H₀: p₁ = p₂ = p₃ = p₄ = .25 vs.H₁: At least one proportion differs from their specified values.

You find the expected value for each cell in a chi-squared test for a contingency table by multiplying the ____________________ total by the ____________________ total and dividing by the sample size,n.

When the problem objective is to describe a population of nominal data with exactly two categories,we can employ either the z-test of a population proportion p,or the chi-squared goodness-of-fit test.

The chi-squared goodness-of-fit test compares the ____________________ frequencies in the table to the ____________________ frequencies based on the null hypothesis.

If we want to conduct a one-tail test of a population proportion,we can employ:

A calculus professor posted the following grade distribution guidelines for her elementary calculus class: 8% A,35% B,40% C,12% D,and 5% F.A sample of 100 elementary statistics grades at the end of last semester showed 12 As,30 Bs,35 Cs,15 Ds,and 8 Fs.Test at the 5% significance level to determine whether the actual grades deviate significantly from the posted grade distribution guidelines.

For comparing two or more populations each having two or more categories,use a(n)____________________ test of a(n)____________________.

If you want to compare two populations that each have two categories,you can use a z-test for two proportions,or a chi-squared test of a(n)____________________.

How do you calculate the expected frequency for one cell in a goodness-of-fit test?

Sales Volumes A telemarketer makes five calls per day.A sample of 200 days gives the frequencies of sales volumes listed below: Number of Sales Observed Frequency (days) 0 10 1 38 2 69 3 03 4 18 5 2 Assume the population is binomial distribution with a probability of purchase p equal to .50. -{Sales Volumes Narrative} Should the assumption of a binomial distribution be rejected at the 5% significance level?

In 2011,computers of Brand A controlled 25% of the market,Brand B 20%,Brand C 10%,and brand D 45%.In 2015,sample data was collected from many randomly selected stores throughout the country.Of the 1,200 computers sold,280 were Brand A,270 were Brand B,90 were Brand C,and 560 were Brand D.Has the market changed since 2011? Test at the 1% significance level.

If the expected frequency e_i for any cell i is less than 5,we should:

The number of degrees of freedom in a chi-squared test for normality,where the number of standardized intervals is 5 and there are 2 population parameters to be estimated from the data,is equal to:

Which statistical technique is appropriate when we wish to analyze the relationship between two qualitative variables with two or more categories?

The test statistic for the chi-squared test of a contingency table is the same as the test statistic for the goodness-of-fit test.

To address whether two variables are related in a contingency table,the alternative hypothesis,H₁,is:

Of the values for a chi-squared test statistic listed below,which one is most likely to lead to rejecting the null hypothesis in a goodness-of-fit test?

Which test(s)can you use when you want to describe a population with two categories?

A chi-squared distribution is symmetric.