Data modeling questions and answers

Recent questions in Modeling data distributions
Chesley 2021-10-26 Answered


A random sample of \(\displaystyle{n}_{{1}}={14}\) winter days in Denver gave a sample mean pollution index \(\displaystyle{x}_{{1}}={43}\).
Previous studies show that \(\displaystyle\sigma_{{1}}={19}\).
For Englewood (a suburb of Denver), a random sample of \(\displaystyle{n}_{{2}}={12}\) winter days gave a sample mean pollution index of \(\displaystyle{x}_{{2}}={37}\).
Previous studies show that \(\displaystyle\sigma_{{2}}={13}\).
Assume the pollution index is normally distributed in both Englewood and Denver.
(a) State the null and alternate hypotheses.
\(\displaystyle{H}_{{0}}:\mu_{{1}}=\mu_{{2}};\mu_{{1}}{>}\mu_{{2}}\)
\(\displaystyle{H}_{{0}}:\mu_{{1}}{<}\mu_{{2}};\mu_{{1}}=\mu_{{2}}\)
\(\displaystyle{H}_{{0}}:\mu_{{1}}=\mu_{{2}};\mu_{{1}}{<}\mu_{{2}}\)
\(\displaystyle{H}_{{0}}:\mu_{{1}}=\mu_{{2}};\mu_{{1}}\ne\mu_{{2}}\)
(b) What sampling distribution will you use? What assumptions are you making?
The Student's t. We assume that both population distributions are approximately normal with known standard deviations.
The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.
The standard normal. We assume that both population distributions are approximately normal with known standard deviations.
The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.
(c) What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate.
(Test the difference \(\displaystyle\mu_{{1}}-\mu_{{2}}\). Round your answer to two decimal places.)
(d) Find (or estimate) the P-value. (Round your answer to four decimal places.)
(e) Based on your answers in parts (i)−(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level \alpha?
At the \(\displaystyle\alpha={0.01}\) level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
At the \(\displaystyle\alpha={0.01}\) level, we reject the null hypothesis and conclude the data are statistically significant.
At the \(\displaystyle\alpha={0.01}\) level, we fail to reject the null hypothesis and conclude the data are statistically significant.
At the \(\displaystyle\alpha={0.01}\) level, we reject the null hypothesis and conclude the data are not statistically significant.
(f) Interpret your conclusion in the context of the application.
Reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Fail to reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver. (g) Find a 99% confidence interval for
\(\displaystyle\mu_{{1}}-\mu_{{2}}\).
(Round your answers to two decimal places.)
lower limit
upper limit
(h) Explain the meaning of the confidence interval in the context of the problem.
Because the interval contains only positive numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.
Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, we can not say that the mean population pollution index for Englewood is different than that of Denver.
Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.
Because the interval contains only negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is less than that of Denver.

Zoe Oneal 2021-10-20 Answered

List 7 ways of representing data

Tyra 2021-10-14 Answered

The following table summarizes the results of a study on SAT prep courses, comparing SAT scores of students in a private preparation class, a high school preparation class, and no preparation class. Use the information from the table to answer the remaining questions.
\(\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{c}\right|}{c}{\mid}\right\rbrace}{h}{l}\in{e}\text{Treatment}&\text{Number of Observations}&\text{Sample Mean}&\text{Sum of Squares (SS)}\backslash{h}{l}\in{e}\text{Private prep class}&{60}&{680}&{265},{500.00}\backslash{h}{l}\in{e}\text{High school prep class}&{60}&{650}&{276},{120.00}\backslash{h}{l}\in{e}\text{No prep class}&{60}&{635}&{302},{670.00}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}\)
Using the data provided, complete the partial ANOVA summary table that follows (Hint: T, the treatment total, can be calculated as the sample mean times the number of observations G, the grand total, can be calculated from the values of T once you have calculated them.)
\(\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{c}\right|}{c}{\mid}\right\rbrace}{h}{l}\in{e}\text{Source}&\text{Sum of Squares (SS)}&{d}{f}&\text{Mean Square (MS)}\backslash{h}{l}\in{e}\text{Between treatments}&&&\backslash{h}{l}\in{e}\text{Within treatments}&&&\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}\)
ANOVA summary tables typically have a "Total" row not induded in the partial table you just completed. Which of the following is a possible reason for induding this row?
a) The \(\displaystyle{M}{S}_{{\to{t}{a}{l}}}\) is used in the calculation of the F test statistic.
b) The \(\displaystyle{S}{S}_{{\to{t}{a}{l}}}\) is used in the calculation of the F test statistic.
c) The total sums of squares is the sometimes called the "error term"
d) The \(\displaystyle{S}{S}_{{\to{t}{a}{l}}}{i}{s}{s}{o}{m}{e}\times{e}{a}{s}{i}{e}{r}\to{c}{a}{l}{c}\underline{{a}}{t}{e}{t}{h}{a}{n}{P}{S}{K}{S}{S}_{{{b}{e}{t}{w}{e}{e}{n}}}\). Since \(\displaystyle{S}{S}_{{{w}{i}{t}{h}\in}}+{S}{S}_{{{b}{e}{t}{w}{e}{e}{n}}}={S}{S}_{{\to{t}{a}{l}}}\), you can use \(\displaystyle{S}{S}_{{\to{t}{a}{l}}}\) to calculate \(\displaystyle{S}{S}_{{{b}{e}{t}{w}{e}{e}{n}}}\).
In ANOVA, the F test statistic is the ? of the between-treatments variance and the within-treatments variance. the value of the F test statistic is ?
When the null hypothesis is true, the F test statistic is ? When the null hypotesis is false, the F test statistic is most likely ? In general, you should reject the null hypotesis for.

Statistics and probability also include various data modeling questions, which can be encountered basically everywhere from Social Sciences and Biology to Engineering and Data Science. Depending on your questions, you can receive immediate help by looking through the data modeling examples that we have presented below for you. These will help you to find solutions and find the answers to presented challenges. It is recommended to model your data carefully and to check things twice to ensure that everything is correct because accuracy is the key to any statistical work where a calculation is involved.
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