Chi-Square Test Questions: Expert Solutions

Why is sample size important when analyzing data?

When performing a log-likelihood ratio test, do I take log to both of the likelihood first or find the ratio first and take the log?

In question I do not get any sigma, I know I can do the t student test based on degrees on freedom if I do not have the population st.dev, but in my case I do not even have the sample st.dev, can it be solved or the teacher made a mistake in the text ?
"The maturation time of maize plants follows the normal distribution. We follow 30 plants and it is seen that they reach maturity in 4 months. Construct a 95% confidence interval for the maturation time of the maize plant population."
In order to find the margin of error i still need S (the sample st.dev) no ?
Otherwise how can i proceed ? Chi squared ?

A restaurant offers 7 different dishes and predicts the dishes will be ordered in the following proportions: 1 (25%), 2 (20%), 3 (10%), 4 (15%), 5 (5%), 6 (6%), 7 (15%).
I am then given the actual proportions in which the dishes are ordered and asked to conduct the appropriate hypothesis test to determine whether the owners' belief regarding the order proportions is correct, then find the p-value (or bounds for the p-value) associated with this test statistic. If I do need to put bounds on the p-value, I'm unsure of how I would go about doing that.

What is the shape of a chi-squared distribution?

What is a chi-squared distribution?

this ${\mathrm{\chi <!--\; \chi \; -->}}_1^2=1.41$ is associated with a one-sided P-value between 0.10 and 0.15
How can i calculate the P-value and why is it one-sided?Is that for ${\mathrm{\chi <!--\; \chi \; -->}}^2$ is a one-tail test?

For how many degrees of freedom is the test statistic proved of significance?
With which realization probability is this or an even greater effect to be expected when the null hypothesis is valid?

IQ scores among the general population have a mean of 100 and a standard deviation of 15. A researcher claims that the standard deviation, o, of IQ scores for males is less than 15. A random sample of 19 IQ scores for males had a mean of 101 and a standard deviation of 10. Assuming that IQ scores for males are approximately normally distributed, is there significant evidence (at the 0.05 level of significance) to conclude that the researcher's claim is correct?
Perform a one-tailed test. Then complete the parts below.
Carry your intermediate computations to three or more decimal places and round your answers as specified below. (If necessary, consult a list of formulas.)
(a) State the null hypothesis ${\displaystyle H_0}$, and the alternative hypothesis ${\displaystyle H_1}$,
${\displaystyle H_0}$:
${\displaystyle H_1}$:
(b) Determine the type of test statistic to use.
(c) Find the value of the test statistic. (Round to three or more decimal places.)
(d) Find the critical value. (Round to three or more decimal places.)
(e) Can we support the claim that the standard deviation of IQ scores for males is less than 15?
a. Yes
b. No

In which of the following situations should the chi-square Test for Homogeneity be used?Select the correct answer below:
A professor wants to determine if the students in each of her two sections had the same distribution of grades. She records the grade distribution for each section and compares the two distributions.
A survey company puts out a survey asking people two questions. First, it asks if a person owns a car or not. Second, it asks whether or not the person supports an upcoming environmental protection bill. The data are recorded in a contingency table. The company wants to determine if support for the bill is independent of car ownership.
A professor expects that the grades on a recent exam are normally distributed with a mean of 80 and a standard deviation of 10. She records the actual distribution of grades and wants to compare it to the normal distribution.

In the following table, likely voters’ preferences of two candidates are cross-classified by gender.
$\begin{array}{|ccc|}\hline & \text{ Male }& \text{ Female }\\ \text{ Candidate A }& 150& 130\\ \text{ Candidate B }& 100& 120\\ \hline\end{array}$
For the chi-square test of independence, the value of the test statistic is:
a. 2.34
b. 1.62
c. 3.25
d. 4

In a chi-square test for goodness of fit, which of the following is used to compute the degrees of freedom?
a. The number of cells in the table
b. The number of categories for the variable plus 1
c. The number of rows times the number of columns
d. The number of categories for the variable minus 1

If the chi-square test is ${\displaystyle {\chi }^2}$(4, N=71)=10, if the alpha is .05, then we ...

In Unit 3 we studied several hypothesis tests: 1-Prop z-Test, 2-Prop z-Test, 1-Sample t-Test, 2- Sample t-Test, Paired t-Test, Chi-Square Goodness-of-Fit Test, and Chi-Square Test for Independence. For each scenario, identify the hypothesis test that should be applied.
1. c) A researcher wants to test a claim that students perform better on math problems when not listening to music as compared to when they do listen to music.
2. d) A researcher wants to test a claim that the average amount of time that kids spend reading books has decreased.
3. e) A researcher wants to test a claim that there is an association between socoal media an mood.

In a chi-square test, the larger the difference between expected and observed frequencies, the more likely you are to:
a. Choose to use a t ratio or some other parametric test
b. Reject the null hypothesis
c. Retain the null hypothesis
d. Use the median test

In a chi-square test, the expected frequencies are:
a. the scores in each cell that would occur if it were due to random chance
b. the scores in each cell that were actually observed in the data
c. The sum of the total scores in each row
d. The sum of the total scores in each column