Chi-Square Test Questions: Expert Solutions

In a flowering plant species, snapdragons, variation in flower color is determined by a single gene. RRgenotype individuals are red, Rr genotype individuals are pink, and rr genotype individuals are white. In a cross between two heterozygous (Rr) individuals, the expected ratio of red:pink:white-flowered offsprings is 1:2:1. Biologists did two cross experiments, and ask whether the results differ significantly from the expected.
(a) The first cross experiment ends up with 40 offsprings, including 10 red, 21 pink, and 9 white.
1. Write the null and alternative hypothesis for the chi-square test.
1. Interpret the p-value and state the conclusion from your test.
(b) The second cross experiment ends up with 4000 offsprings, including 1000 red, 2100 pink, and 900 white.
1. This time, can you reject the null hypothesis? why?
1. (Bonus question) Do the proportions of observed data in two experiments differ? Did the chi-square test results from these two experiments differ? Why?

In the Salsberry (2003) study shared in this weeks module, the researcher presents the following results of the statistical analysis: "With respect to family configuration, 20% of the children enrolled in Medicaid, 29% of the uninsured children, and 44% of the privately insured children were in families where the adults were in a “partnered relationship”, ${\displaystyle [{\chi }^2(2,N=392)=21.95;P=.0001]}$" What type of analysis does this statement reflect?

In 2010, a medical research group reported the results of an experiment to evaluate the effectiveness of acupuncture to treat a chronic intestinal condition. A group of volunteers with the chronic intestinal condition agreed to participate in the experiment and be randomly assigned to either a true acupuncture treatment or a placebo treatment. The placebo treatment mimicked the application of acupuncture, but no needle penetrated the skin. Random assignment resulted in 78 subjects receiving acupuncture and 75 subjects receiving the placebo treatment. After receiving 6 treatments over the course of 3 weeks, patients were asked to report whether they had experienced a reduction in the chronic intestinal condition. The table summarizes the data from the study, with expected cell counts in parentheses.
$\begin{array}{|cccc|}\hline & \text{ Yes }& \text{ No }& \text{ Total }\\ \text{ Acupuncture }& 41(37.2)& 37(40.8)& 78\\ \text{ Placebo treatment }& 32(35.8)& 43(39.2)& 75\\ \text{ Total }& 73& 80& 153\\ \hline\end{array}$
Which of the following is true about the chi-square test for homogeneity?
A)The number of subjects randomly assigned to each treatment is not the same; therefore, it is not appropriate to use a chi-square test for homogeneity across treatment groups.
B)Volunteers do not constitute a random sample from the population of all patients with the chronic intestinal condition; therefore, it is not appropriate to use a chi-square test for homogeneity across treatment groups.
C)Volunteers with the chronic intestinal condition were randomly assigned to each treatment, so the independence condition has been met.
D)Not all of the observed cell counts are large enough to satisfy the conditions for applying the chi-square test of homogeneity.
E)Not all of the expected cell counts are large enough to satisfy the conditions for applying the chi-square test for homogeneity.

If we have conducted a chi-square test, then the type of data is
a. One Nominal variable samp; one Ordinal variable
b. One Nominal variable samp; one Numerical variable
c. Both Nominal variables
d. Both Numerical variables

So called "dating" apps like Tinder and Grindr have become known to many as “hook-up" apps. You want to know if people using these apps for "dating" or "hook-ups" is significantly different by gender-identity. You survey 200 users of Tinder to get data on their gender-identity and if they are on the app for dating/looking for a relationship or hook-ups/not looking for a relationship. Is there an association between gender and goals motive for using Tinder?
What type of hypothesis test is most appropriate?

Please specify the statistical test which would be most suitable for the situations below:
A possible association between smoking (yes/no) and snoring (yes/no) should be investigated.
An educating video is prepared for people about wearing a safety belt while driving. Their safety belt wearing habits were assessed before watching the video and re-assessed after a month of watching the educating video (n=17).

We have studied 2 different test statistics, z, and X2. Explain the similarities in;
1. How each test statistic is calculated
2. How each test statistic is used to determine if the sample statistic provides enough evidence against the null hypothesis to reject it.
*i saw another answer on here but it didn't go in depth so im still confused

The following table shows age distribution and location of a random sample of 166 buffalo in a national park.
$\begin{array}{|ccccc|}\hline \text{ Age }& \text{ Lamar District }& \text{ Nez Perce District }& \text{ Firehole District }& \text{ Row Total }\\ \text{ Calf }& 15& 16& 10& 41\\ \text{ Yearling }& 12& 11& 10& 33\\ \text{ Adult }& 35& 29& 28& 92\\ \text{ Column Total }& 62& 56& 48& 166\\ \hline\end{array}$
Use a chi-square test to determine if age distribution and location are independent at the 0.05 level of significance.
1. Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)
2. What are the degrees of freedom?

Observed and Expected counts are given for a chi-square test for association, with the Expected counts in parentheses. Calculate the chi-square statistic for this test.
$\begin{array}{|cccc|}\hline & \text{ A }& \text{ B }& \text{ C }\\ 1& 33(40.4)& 34(31.6)& 33(28)\\ 2& 22(40.4)& 51(31.6)& 27(28)\\ 3& 147(121.2)& 73(94.8)& 80(84)\\ \hline\end{array}$
Round your answer to three decimal places.
${\displaystyle {\chi }^2=}$

Is age group related to the device people prefer to use to watch television? A research firm sought to answer this question by surveying a random sample of 260 U.S. adults age 18 and over. The results are shown below.
$\begin{array}{|ccccc|}\hline & & \text{Device}& & \\ & & \text{Television}& \text{Computer}& \text{Mobile device}\\ & 18-24& 19& 6& 12\\ \text{Age Group}& 25-34& 23& 7& 39\\ & 35-54& 34& 8& 28\\ & 55+& 33& 8& 13\\ \hline\end{array}$
Which of the following tests should be used?
Either (a) or (c).
A chi-square goodness of fit test.
A z-test for the difference of two proportions.
A chi-square test for homogeneity.
A chi-square test for independence.

In which situations should a researcher use a chi-square test instead of a correlation or t-test to conduct a hypothesis test? When should a chi-square goodness of fit test be used relative to a chi-square test for independence?

In order for you to use the goodnees-of-fit test, the test of independence, or the test of homogeneity, the expected frequencies for each cell needs to be at least

In the context of outbreak of COVID – 19, a sample of 200 patients are selected. Out of them, 100 were given a drug and the others were not given any drug. The results are as follows:
$\begin{array}{cc}& \text{Number of patients}\\ & \begin{array}{|cccc|}\hline & \text{ Drug }& \text{ No Drug }& \text{ Total }\\ \text{ Cured }& 65& 55& 120\\ \text{ Not cured }& 35& 45& 80\\ \text{ Total }& 100& 100& 200\\ \hline\end{array}\end{array}$
Test whether the drug is effective or not. (The Chi-square value as 5% level of significance for 1 degree of freedom is 3.841)

If I had the questions
What is your ethnicity?
And how much do you spend per week on food? On a survey where I collected 40 responses
Which of the following tests would I be able to run using my data?
a. Correlation
b. Regression
c. ANOVA
d. t-test
e. Chi- square

The manager of a computer network has collected data on the number of times that service has been interrupted on each day over the past 500 days. The results are as follows as shown in the table.
Does this distribution of service interruptions follow the expected percentages which are 0=30%, 1=30%, 2= 20%, 3=12%, 4=3%, 5=3%, and 6=2%? Use the 0.01 level of significance.
$\begin{array}{|cc|}\hline \text{ Interruptions per Day }& \text{ Number of Days }\\ 0& 160\\ 1& 175\\ 2& 86\\ 3& 41\\ 4& 18\\ 5& 12\\ 6& 8\\ \hline\end{array}$
1. What type of hypothesis testing should be used?
a. Chi-square Goodness of Fit Test
b. Chi-square Test on Independence
2. What are the null and alternative hypothesis?
a. ${\displaystyle H_0}$: The observed frequency does not follow the expected distribution; ${\displaystyle H_1}$: the observed frequency follows the expected distribution
b. ${\displaystyle H_0}$: The observed frequency follows the expected distribution; ${\displaystyle H_1}$: The observed frequency does not follow the expected distribution
3. What are the significance level and the type of test?
a. ${\displaystyle \alpha =0.01}$, Right-tailed
b. ${\displaystyle \alpha =0.01}$, left-tailed
c. ${\displaystyle \alpha =0.01}$, two-tailed

The following Table contains information from a survey among 599 participants classified according to their age groups. The second column shows the percentage of obese people per age class among the study participants. The last column comes from a different study at the national level that shows the corresponding percentages of obese people in the same age classes in the UK. Perform a Hypothesis test at the 5% significance level to determine whether the survey participants are a representative sample of the UK obese population.
$\begin{array}{|ccc|}\hline \text{ Age Class (Years) }& \text{ Obese (Percentage) }& \text{ Expected UK average (percentage) }\\ 20–30& 65.0& 32.6\\ 31–40& 26.5& 32.6\\ 41–50& 13.6& 36.6\\ 51–60& 21.9& 36.6\\ 61–70& 21.0& 39.7\\ \hline\end{array}$

We can make a causal claim from the results of the chi-square test ? tru or false

Value of test statistic Chi square is 6.435 and critical value of Chi square from the table is 6.345; thus we will reject the null hypothesis (H0).
Select one:
a.True
B.False

The Gambler's Fallacy is the idea that past events can affect future behavior. The fallacy often generates real financial consequences for those who like to take their chances at gambling, which, in turn, reaps financial benefits for gambling businesses like casinos or race tracks.
Being a person who enjoys playing dice games, you want to test the Gambler's Fallacy using a six-sided die. You toss the die 300 times with the following results.
$\begin{array}{|ccccccc|}\hline \text{ Roll }& 1& 2& 3& 4& 5& 6\\ \text{ Frequency }& 54& 49& 50& 51& 51& 45\\ \hline\end{array}$
Find the value of the chi-square test statistic for this scenario.

What are your suggestions on performing a qui-square test?
a. when you have to perform a qui-square Goodness of Fit Test.
b. when you have to perform a qui-square Independence Test.
Mention the conditions that must be met in order to perform both tests..