Improve Your Understanding of College Level Statistics Problems

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

Point and interval estimation of normal variance ${\displaystyle \theta }$ when the mean ${\displaystyle \mu }$ is known.
Let ${\displaystyle X_1,\dots ,X_n}$ are independent observations over the random variable ${\displaystyle X_i\sim N(\mu ,\theta )}$ where ${\displaystyle \mu }$ is known and ${\displaystyle \theta >0}$. We are given the following estimator for ${\displaystyle tehta}$:
${\displaystyle \hat{\theta }=\frac{\sum _{i=1}^n\left\{{(X_i-\mu )}^2\right\}}{\theta }}$

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 each of Exercises, we have provided a sample mean, sample standard deviation, and sample size. In each case, use the one-mean t-test to perform the required hypothesis test at the 5% significance level.
x = 24, s = 4, n = 15, H0: ${\displaystyle \mu }$ = 22, Ha: ${\displaystyle \mu }$ > 22

In a statistics class of 30 students, the mean score on the midterm was 72. In another class of 40 students, the mean score was 79. What was the mean score of the two classes combined?

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 a statistics class of 100 students, the mean score on the midterm was 98. In another class of 23 students, the mean score was 8. What was the mean score of the two classes combined?

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

If the median of the data below is 43, what is a possible value of x: 25, 34, 46, 43, 77, 68, x?

How to calculate confidence interval for dice hits?
There is a dice with e edges [1;e]. The dice rolls in a one experiment r times. Thus the edge numbered 1 can be generated in this experiment from 0 to r times. I need to calculate theoretical 95% confidence interval for this count.

Is a ${\displaystyle 99\mathrm{\%}}$ upper confidence bound the upper limit of a ${\displaystyle 99\mathrm{\%}}$ confidence interval?

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 a statistics class of 10 students, the mean score on the midterm was 702. In another class of 700 students, the mean score was 19. What was the mean score of the two classes combined?

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