**Investigating Class Sizes Between Portland and Beaverton School Districts**A school administrator aims to determine if there is a significant difference in the number of students per class for Portland Public School district (group 1) compared to the Beaverton School district (group 2). We assume that the populations are normally distributed but with unequal variances. ### Data Collected:- **Portland School District**: - Sample Size (n1): 28 classes - Sample Mean (x̄1): 36 students per class - Standard Deviation (s1): 5- **Beaverton School District**: - Sample Size (n2): 27 classes - Sample Mean (x̄2): 35 students per class - Standard Deviation (s2): 6### Objective:To find a 90% confidence interval for the difference of the means (µ1 - µ2). Utilize technology to find the critical value with degrees of freedom (df) calculated to be approximately 50.6214. The final interval should be rounded to 4 decimal places.### Confidence Interval Calculation:Use the following formula for the confidence interval of the difference of means with unequal variances:\[ CI = (\bar{x1} - \bar{x2}) \pm t_{\alpha/2, df} \times \sqrt{\frac{s1^2}{n1} + \frac{s2^2}{n2}} \]Where:- $ \bar{x1} $ and $ \bar{x2} $ are the sample means- $ s1 $ and $ s2 $ are the standard deviations- $ n1 $ and $ n2 $ are the sample sizes- $ t_{\alpha/2, df} $ is the critical value from the t-distribution for the specified confidence level and degrees of freedom.Insert the calculated critical value below:\[ < \mu1 - \mu2 < \]-----------------This detailed explanation will help students understand how to compare two means from different groups, accounting for unequal variances, using confidence intervals.

The confidence interval measures the range where the true parameter occurs. It has two parts, they…

Answered: A school administrator wants to see if…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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An educator has developed a program to improve math scores on the Texas STAAR test. The average STAAR mathematics test for the third graders in the district was mean of 1472. A sample of n=30 third graders took the new math training program before taking the STAAR Math test. The average score for the students was M= 1497 with a standard deviation of 145. (note the standard deviaiton is not a variance). Was there a significant change in test scores (Use standard deviaiton = 0.05, two tailed test). Determine the t crit value.
An economist was curious if the mean yearly amount of seafood consumed in Sweden is significantly different than the mean yearly consumption in the United States. They randomly selected 125 citizens in Sweden and determined their sample mean is 12 kg with a standard deviation of 5.2 kg. The 140 randomly selected U.S. citizens had a sample mean of 9.7 kg with a standard deviation of 5.8 kg. Is this sufficient evidence to say that the mean consumption is different? Which are the correct hypothesis statements for this situation? Hoμs Hus HAμs=Pus H。 ¦ µ¸ = Pus HAμs Hus Hoµs=Pus HAHs>Hus Hop=0.10 ΗΑ : μ > 0. 10
A study was being done at our District to see who takes more units per semester, students at Cypress College or students at number of units they took per semester was 13.1 units with a standard deviation of 2.4 units. They randomly selected a sample of 65 Cypress College students and found that the mean number of units they took per semester was 11.6 units with a standard Fullerton College. To test this, the researchers randomly selected 60 Fullerton College students and found that the mean deviation of 3.7 units. Test the claim that the mean number of units is more for Fullerton College students than Cypress College students at the a=0.05 level of significance. Calculator Function [ Select ] [ Select ] X^2-Test T-Test 2-SampFTest 2-PropZTest ANOVA 2-SampT Test [ Select ] sufficient evidence that the mean number of units is (Select] for Fullerton College students than Cypress College students.
Many cheeses are produced in the shape of a wheel. Because of the differences in consistency between these different types of cheese, the amount of cheese, measured by weight, varies from wheel to wheel. Heidi Cembert wishes to determine whether there is a significant difference, at the 10% level, between the weight per wheel of Gouda and Brie cheese. She randomly samples 18 wheels of Gouda and finds the mean is 1.3 lb with a standard deviation of 0.3 lb; she then randomly samples 10 wheels of Brie and finds a mean of 0.95 lb and a standard deviation of 0.21 lb. What is the df and p-value for Heidi's hypothesis of equality? Assume normality. (Give your answer correct to four decimal places.)
Salvatore, as the director of a regional bank, is concerned about the wait times of customers at the four branches. He randomly selects 48 patrons at each branch and records the waiting time for each patron. The results of the samples are shown below. The Alvrine branch has a mean waiting time of 13.49 minutes with a standard deviation of 1.97 minutes.The Durham branch has a mean waiting time of 12.61 minutes with a standard deviation of 2.89 minutes.The Hanover branch has a mean waiting time of 11.06 minutes with a standard deviation of 2.46 minutes.The Mascomonet branch has a mean waiting time of 12.89 minutes with a standard deviation of 3.12 minutes.
The salaries of professional baseball players are heavily skewed right with a mean of $3.2 million and a standard deviation of $2 million. The salaries of professional football players are also heavily skewed right with a mean of $1.9 million and a standard deviation of $1.5 million. A random sample of 40 baseball players' salaries and 35 football players' salaries is selected. The mean salary is determined for both samples. Let 1,-i, represent the difference in the mean salaries for baseball and football players. Which of the following represents the mean of the sampling distribution for ī, -7,? -1.3 1.3 1.9 3.2
Insurance Company A claims that its customers pay less for car insurance, on average, than customers of its competitor, Company B. You wonder if this is true, so you decide to compare the average monthly costs of similar insurance policies from the two companies. For a random sample of 7 people who buy insurance from Company A, the mean cost is $150 per month with a standard deviation of $16. For 12 randomly selected customers of Company B, you find that they pay a mean of $160 per month with a standard deviation of $14. Assume that both populations are approximately normal and that the population variances are equal to test Company A's claim at the 0.10 level of significance. Let customers of Company A be Population 1 and let customers of Company B be Population 2. Step 2 of 3: Compute the value of the test statistic. Round your answer to three decimal places.
According to a news program, Americans take an average of 4.9 days off per year because of illness. The manager of a large chain of grocery stores wants to know if the employees at the grocery store, on average, take fewer days off than the national average. The manager selects a random sample of 80 employees in the company and found the sample mean number of days off for the 80 employees was 4.75 days with a standard deviation of 0.9 days. When the manager performed a significance test, the P-value was 0.07. What is the meaning of this P-value in context?
Insurance Company A claims that its customers pay less for car insurance, on average, than customers of its competitor, Company B. You wonder if this is true, so you decide to compare the average monthly costs of similar insurance policies from the two companies. For a random sample of 13 people who buy insurance from Company A, the mean cost is $150 per month with a standard deviation of $19. For 9 randomly selected customers of Company B, you find that they pay a mean of $157 per month with a standard deviation of $16. Assume that both populations are approximately normal and that the population variances are equal to test Company A's claim at the 0.05 level of significance. Let customers of Company A be Population 1 and let customers of Company B be Population 2. Step 1 of 3: State the null and alternative hypotheses for the test. Fill in the blank below. Ho: M₁ = μ₂ Ha:M₁ •H₂
An educator has developed a program to improve math scores on the Texas STAAR test. The average STAAR Mathematics test for the third graders in the district was a mean= 1472. A sample of n= 30 third graders took the new math training prgram before taking the STAAR Math test. The average score for the students was M= 1497. with a standard deviation of s= 145 (note, this is standard deviation, not variance). Was there a significant change in test scores ( use stard devistion of 0.05, two tail test). Calculate the effect size using Cohen's d.
A pharmaceutical company needs to know if its new cholesterol drug, Praxor, is effective at lowering cholesterol levels. It believes that people who take Praxor will average a greater decrease in cholesterol level than people taking a placebo. After the experiment is complete, the researchers find that the 46 participants in the treatment group lowered their cholesterol levels by a mean of 19.5 points with a standard deviation of 4.9 points. The 37 participants in the control group lowered their cholesterol levels by a mean of 18.4 points with a standard deviation of 4.1 points. Assume that the population variances are not equal and test the company's claim at the 0.02 level. Let the treatment group be Population 1 and let the control group be Population 2. Step 2 of 3: Compute the value of the test statistic. Round your answer to three decimal places.
According to Kaiser Family Foundation survey in 2011 and 2010, the average premium for employer-sponsored health insurance for family coverage was $15,073 in 2011 and $13,770 in 2010 (USA TODAY, September 29, 2011). Suppose that these averages were based on random samples of 250 and 200 employees who had such employer-sponsored health insurance plans for 2011 and 2010, respectively. Further assume that the population standard deviations for 2011 and 2010 were $2160 and $1990, respectively.

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