Practice Math Statistics Problems and Master the Concepts

If the joint probability density function of two continuous random variables X and Y isgiven by f(x; y) = 2, 0 < y < 3x, 0 < x < 1;find,(a) f(y/x),(b) E(Y/x), (c) Var(Y/x).

Damian Hanna 2022-03-08

Why would we want to use a Chi Squared Test for this study? What are the best ways to describe the data graphically and numerically?
An investigation of the association between drink preferences and the color of teeth is proposed. Subjects will be surveyed as to the type of drink most often consumed (coffee/tea. Juice, caramel-colored soda, water, or milk). A clinical exam will be performed after dental cleaning to determine the color of the teeth (reddish brown, reddish yellow, gray, reddish gray).

Pelizzolaf40 2022-03-08

Wilson interval with zero trials
I'm calculating Wilson score interval for some number of trials, so I have a question:
is it correct to assume this interval as [0 , 1] when you have zero trials?

meiprate81w 2022-03-08

You are conducting a multinomial hypothesis test for the claim that all 5 categories are equally likely to be selected. Complete the table.
$\begin{array}{cc} Category & Observed Frequency & Expected Frequency & Squared Pearson Residual \\ A & 18 \\ B & 10 \\ C & 15 \\ D & 17 \\ E & 17 \end{array}$
What is the chi-square test-statistic for this data?
$χ^{2} =$
Report all answers accurate to three decimal places.

friasrodixg 2022-03-08

You are conducting a test of homogeneity for the claim that two different populations have the same proportions of the following two characteristics. Here is the sample data.
$\begin{array}{cc} Category & Population #1 & Population #2 \\ A & 36 & 125 \\ B & 22 & 68 \end{array}$
What is the chi-square test-statistic for this data?
$χ^{2} =$
Report all answers accurate to three decimal places.

Juliet Jackson 2022-03-07

You obtain a sample chi-square value of $χ^{2} = - 5.49$ . On the basis of this value, you know that
a. there is a negative association between your two variables.
b. the observed frequencies are higher than the expected frequencies across at least half of your cells.
c. you have made a calculation error; chi-square values cannot be negative.
d. the observed frequencies are lower than the expected frequencies across all cells.

Noelle King 2022-03-07

You intend to conduct a test of homogeneity for a contingency table with 8 categories in the column variable and 2 categories in the row variable. You collect data from 352 subjects.
What are the degrees of freedom for the $χ^{2}$ distribution for this test?

adoliremdhp 2022-03-07

You are conducting a multinomial hypothesis test ( $α = 0.05$ ) for the claim that all 5 categories are equally likely to be selected.
$\begin{array}{cc} Category & Observed Frequency \\ A & 25 \\ B & 13 \\ C & 21 \\ D & 8 \\ E & 9 \end{array}$
What is the chi-square test-statistic for this data?
$χ^{2} =$

Find the density of random vairable Z=X+Y, whare X and Y two independent uniform random vairableS over (-1, 1)?

Jerimiah Hansen 2022-03-06

Your state is going to vote on becoming a "right to work" state in the next, and you wonder if there is there a relationship between salary levels and unionization. You find data on salary from the U.S. Census, which is split into three groups: Low; Moderate/About Average, and; High. To see if salary, measured in this way, is associated with unionization you find a variable in the same dataset called "UNION", which has two categories: the respondent has a unionized job and the respondent does not have a unionized job. Because you want to know if you should favor or oppose becoming a "right to work" state, you test these two variables to see if there is an association between salary level and unionized labor.
What type of hypothesis test is most appropriate?

chatarazona7sq 2022-03-06

You are dnalyzingresuits Tor cupcake restaurant. Ine stuay aims to determine if the cupcake sales have increased. What would be the most approprite signicance level for hypothesis tests for this type of study?1.00.050.010.001O

Dawson Riggs 2022-03-06

You are conducting a test of independence for the daim that there is an association between morning beverage and age.
$\begin{array}{cc} Juice & Coffee & Pop & Tea \\ less that 25 & 19 & 18 & 5 & 32 \\ 25 or older & 27 & 30 & 2 & 43 \end{array}$
What is the chi-square test-statistic and the corresponding p-value for this data?
$χ^{2} = ?$ , [three decimal accuracy]
p-value=?, [three decimal accuracy]

Juliet Jackson 2022-03-06

You are conducting a test of independence for the claim that there is an association between the row variable and the column variable.
$\begin{array}{cccc} X & Y & Z \\ A & 35 & 29 & 6 \\ B & 53 & 38 & 5 \end{array}$
The expected observations for this table would be
$\begin{array}{cccc} X & Y & Z \\ A \\ B \end{array}$
What is the chi-square test-statistic for this data? (2 decimals) $χ^{2} = ◻$
Report all answers accurate to two decimal places.

Coby Allison 2022-03-04

$\begin{matrix} Brand of Smartphone & Male \\ A & 43 \\ B & 34 \\ C & 48 \end{matrix}$
A. What is the value for the degrees of freedom?
B. If the expected number of males with smartphone brand B is 32.5, what is the chi-square component?
C. If the test statistic (chi-square) = 6.40, then the p-value =
D. If the significance level was 0.05, should the researcher reject or fail to reject the null?

haugmbd 2022-03-04

$\begin{array}{cc} Subgroup of Participants & Supine SBP Mean (SD) & Standing SBP Mean (SD) & Percent with > 5.0 Decrease & Percent with > 5.0 Increase \\ White women (N = 301) & 120.4 (18.4) & 120.0 (18.8) & 32.6 % & 32.2 % \\ African-American women (N = 107) & 122.7 (19.3) & 122.8 (19.4) & 30.2 % 31.9 % \\ White men (N = 339) & 121.2 (18.9) & 120.2 (19.9) & 39.5 % & 25.6 % \\ African-American men (N = 95) & 124.7 (20.4) & 125.9 (21.6) & 13.7 % & 51.3 % \\ Total (N = 842) & 121.5 (19.0) & 121.1 (19.5) & 29.8 % \end{array}$
Would it be possible to analyze data in table 2 with a chi-square test? if yes, specify how

Adrienne Rowe 2022-03-04

$\begin{matrix} Children at home? \\ Observed & \begin{array}{ccc} College Major & Yes & No & Totals \\ Applied Behavioral Science & 30 & 10 & 40 \\ Criminal Justice & 10 & 7 & 17 \\ Political Science & 10 & 10 & 20 \\ Psychology & 32 & 11 & 43 \\ Totals & 82 & 38 & 129 \\ χ^{2} = 5.37 \end{array} \end{matrix}$
1. How many variables are involved in this chi-square test?
2. Which type of chi-square test is this? Goodness of Fit or Test of Independence
3. How many degrees of freedom are involved?
4. Using the chi-square critical values table, is the result of this test statistically significant? Yes or No

embeucadaoo8 2022-03-04

750 units of product are produced in 3 different production lines. It is desired to investigate whether there is a difference between the production lines at the 95% confidence level. Find the chi-square calculation value.
a. 514
b. 20
c. 45
d. 34
$\begin{array}{cc} Production line & Observed & Expected \\ A & 250 & 250 \\ B & 200 & 250 \\ C & 300^{2} 50 \\ Total & 750 & 750 \end{array}$

Reginald Owens 2022-03-04

(a) In formulating hypotheses for a statistical test of significance, the null hypothesis is often
A. the probability of observing the data you actually obtained
B. a statement that the data are all 0.
C. a statement of ''no effect'' or ''no difference''.
D. 0.05
(b) In testing hypotheses, which of the following would be strong evidence against the null hypothesis?
A. Using a small level of significance.
B. Obtaining data with a large P -value.
C. Obtaining data with a small P -value.
D. Using a large level of significance.
(c) The P -value of a test of a null hypothesis is
A. the probability, assuming the null hypothesis is false, that the test statistic will take a value at least as extreme as that actually observed.
B. the probability the null hypothesis is false.
C. the probability the null hypothesis is true.
D. the probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as that actually observed.

Lubna Boyce 2022-03-04

The level of signifñicance (usually.05) associated with a significance test is the probability,
A. That the alternative hypothesis is true.
B. That the null hypothesis is true.
C. Of not rejecting a true null hypothesis.
D. Of rejecting a true null hypothesis.

Harken43 2022-03-04

A study done by Dr. S. Friedler, a trained mime and a physician, found evidence that being entertained by live clowns immediately after in-vitro fertilization (IVF) may increase conception rates (Friedler et al, 2011) DOI: 10.1016. Yes, this real study was about whether watching 15 minutes of ‘medical clowning’ after an embryo transfer or IVF would affect the chance of a successful pregnancy. The 186 women in the study were randomly assigned to either clown or no clown condition. Please use these data to test whether pregnancy rates were independent of being entertained by a clown after IVF. Show your work and include each step in the hypothesis testing process.
$\begin{array}{cc} Observed data: & Pregnant & Not Pregnant \\ Clown & 33 & 60 \\ No Clown & 18 & 75 \end{array}$
a. State the null and alt hypotheses.
b. Find df and critical value for the chi-square test.
c. Calculate the expected frequencies and the chi-square test value. Is it significant?
d. Write an APA conclusion based on the results of the test.

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