### Educational Material: College Entrance Exam and Mathematics Readiness**Scenario:**A college entrance exam company determined that a score of 24 on the mathematics portion of the exam suggests that a student is ready for college-level mathematics. To achieve this goal, the company recommends that students take a core curriculum of math courses in high school. Suppose a random sample of 250 students who completed this core set of courses results in a mean math score of 24.4 on the college entrance exam with a standard deviation of 3.1. Do these results suggest that students who complete the core curriculum are ready for college-level mathematics? That is, are they scoring above 24 on the mathematics portion of the exam?**Tasks:**a) **State the appropriate null and alternative hypotheses. Fill in the correct answers below.****Explanation of Hypotheses:**- **Null Hypothesis (H₀):** This is the hypothesis that there is no significant difference or effect. In this context, it means the mean score of students who completed the core curriculum is equal to 24.- **Alternative Hypothesis (H₁):** This is the hypothesis that there is a significant difference or effect. Here, it would mean that the mean score is greater than 24.**Mathematical Notation:**- $ H₀: \mu = 24 $- $ H₁: \mu > 24 $---**Interactive Elements:**- **Help me solve this:** Assistance option for solving hypothesis testing problems.- **View an example:** Provides an example problem with solutions.- **Get more help:** Directs to additional resources or tutorials on the subject.- **Clear all:** Clears all inputs for a fresh start.- **Check answer:** Validates your input and provides feedback.---**Additional Information:**- **Sample Size (n):** 250 students- **Sample Mean (x̄):** 24.4- **Standard Deviation (σ):** 3.1**Date and Settings displayed:**- **Time:** 1:18 PM- **Temperature:** 94°F- **Weather:** Mostly sunny- **Date:** 6/18/2022- **Device Details:** HP laptop with icons for various browsers and applications visible.This educational scenario provides a clear example of how statistical hypotheses are formulated and tested using sample data. It highlights critical thinking

According to the given information in this question We need to identify the null hypothesis and…

Answered: A college entrance exam company…

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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A college entrance exam company determined that a score of 23 on the mathematics portion of the exam suggests that a student is ready for college-level mathematics. To achieve this goal, the company recommends that students take a core curriculum of math courses in high school. Suppose a random sample of 250 students who completed this core set of courses results in a mean math score of 23.2 on the college entrance exam with a standard deviation of 3.7. Do these results suggest that students who complete the core curriculum are ready for college-level mathematics? That is, are they scoring above 23 on the mathematics portion of the exam? Complete parts a) through d) below. Click the icon to view the table of critical t-values. ... (a) State the appropriate null and alternative hypotheses. Fill in the correct answers below. The appropriate null and alternative hypotheses are H,: versus H,: (Type integers or decimals. Do not round.) (b) Verify that the requirements to perform the test…
A USA based cable broadband company wants to investigate whether it's east coasts customers have a higher average customer satisfaction score than compared to it's west coast customers. The customer survey asks for a score between 1 and 5, with 1 being poor and 5 being excellent. 174 east coast customers are surveyed, and the sample mean is 3.35 with a sample standard deviation of 0.51. For the west coast, 355 customers are surveyed, and the sample mean is 3.24 with a sample standard deviation of 0.52.
The manager of the shipping department of a mail-order operation located in New York advertises that the length of time it takes for customers in California to receive their orders is 8 days. However, the office has been receiving complaints from customers in California stating that orders do not arrive in time advertised. To learn more about this potential problem, the manager chose a random sample of 15 orders. The sample mean of delivery times was 12.25 days. The sample standard deviation was 3.67 days.The average time it takes for all California customers to receive their orders is to be estimated with a 99% confidence interval. a. The ? − or ? −value that should be used to construct this interval is b. The margin of error is equal to
The Chartered Financial Analyst (CFA) designation is fast becoming a requirement for serious investment professionals. Although it requires a successful completion of three levels of grueling exams, it also entails promising careers with lucrative salaries. A student of finance is curious about the average salary of a CFA charterholder. He takes a random sample of 36 recent charterholders and computes a mean salary of $129,000 with a standard deviation of $22,000. Use this sample information to determine the 99% confidence interval for the average salary of a CFA charterholder. (You may find it useful to reference the t table. Round final answers to the nearest whole number.) Confidence interval
A college entrance exam company determined that a score of 23 on the mathematics portion of the exam suggests that a student is ready for college-level mathematics. To achieve this goal, the company recommends that students take a core curriculum of math courses in high school. Suppose a random sample of 150 students who completed this core set of courses results in a mean math score of 23.7 on the college entrance exam with a standard deviation of 3.7. Do these results suggest that students who complete the core curriculum are ready for college-level mathematics? That is, are they scoring above 23 on the math portion of the exam? Complete parts a) through d) below. b) Verify that the requirements to perform the test using the t-distribution are satisfied. Check all that apply. A. The students were randomly sampled. B. The students' test scores were independent of one another. C. The sample size is larger than 30. D. None of the requirements are satisfied.
The Chartered Financial Analyst (CFA) designation is fast becoming a requirement for serious investment professionals. Although it requires a successful completion of three levels of grueling exams, it also entails promising careers with lucrative salaries. A student of finance is curious about the average salary of a CFA charterholder. He takes a random sample of 36 recent charterholders and computes a mean salary of $129,000 with a standard deviation of $22,000. Use this sample information to determine the 99% confidence interval for the average salary of a CFA charterholder. (You may find it useful to reference the t table. Round final answers to the nearest whole number.)
According to a recent study published by the American Statistics for Educators Journal, statistics students spend, on average, 80 minutes a week playing video games. A certain instructor of statistics at WCC believes that WCC students spend less than this amount of time playing video games per week. To test his belief, he randomly samples 31 students and finds the sample mean to be 72 minutes with a standard deviation of 35 minutes. At the 0.05 level of significance, is there evidence to suggest that WCC students spend less than 80 minutes a week, on average, playing video games? Use the p-value approach. Define the parameter we are testing and setup a hypothesis to test the see if the statistics instructor is correct: Calculate the test statistics for this hypothesis test. What is the p-value for this hypothesis test?
An ordinary traveler claims that the average difference between the plane fares of all trips from the Philippines to a certain destination in the two airlines is significantly different. To validate this claim, 145 trips have been randomly selected from the first airline, which gave a mean fare of PHP 23,502.71 with a sample standard deviation of PHP 4,853.39. On the other hand, 123 trips are chosen at random from the second airline, which provided a mean fare of PHP 21,884.09 with a sample standard deviation of PHP 4,987.73. Assume that the populations are normally distributed, and the standard deviations for both populations are equal. At ? = 0.01, indicate whether or not there is sufficient evidence to support the traveler’s claim
The Chartered Financial Analyst (CFA) designation is fast becoming a requirement for serious investment professionals. It is an attractive alternative to getting an MBA for students wanting a career in investment. A student of finance is curious to know if a CFA designation is a more lucrative option than an MBA. He collects data on 38 recent CFAs with a mean salary of $138,000 and a standard deviation of $34,000. A sample of 80 MBAs results in a mean salary of $130,000 with a standard deviation of $46,000.a) Specify the hypotheses to test whether a CFA designation is more lucrative than an MBA.b) Calculate the value of the test statistic and the p-value. Do not assume that the population variances are equal.c) At the 5% significance level, is a CFA designation more lucrative than an MBA?
The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures students' study habits and attitudes toward school. The survey yields several scores, one of which measures student attitudes toward studying. The mean student attitude score for college students is about 30, and standard deviation is about 12. A researcher in the Philippines is concerned about the declining performance of college graduates on professional licensure and board exams. She suspects that poor attitudes of students are partly responsible for the decline and that the mean for college seniors who plan to take professional licensure or board exams is less than 30. She gives the SSHA to an SRS of 144 college seniors in the Philippines who plan to take professional licensure or board exams. Suppose we know that the student attitude scores in the population of such students are Normally distributed with standard deviation σ = 12. (a) We seek evidence against the claim that μ = 30. What is the…
In a sample of 351 gamers between the ages of 16-25, the mean number of hours spent gaming per week was 42.5 hours. In a sample of 269 gamers between the ages of 26-40, the mean number of hours spent gaming per week was 43.8 hours. If the population standard deviation for the mean number of hours spent gaming per week is 9.5 for the age group 16-25 and 10.7 for the age group 26-40, test the claim that gamers between the ages of 16-25 spend less time gaming per week than gamers between the ages of 26-40. Assume α=0.03. Let population 1 be gamers in the age group 16-25 and population 2 be gamers in the age group 26-40. Round the test statistic to two decimal places, and round the p-value to four decimal places. The test statistic is . The p-value is . Should the null hypothesis be rejected?
Assume a media agency reports that it takes television streaming service subscribers in the U.S. an average of 6.60 days to watch the entire first season of a television series, with a standard deviation of 4.21 days. Scarlett is an analyst for an online television and movie streaming service company that targets to the 18-50 age bracket. She wants to determine if her company's customers exhibit shorter viewing rates for their series offerings. Scarlett plans to conduct a one-sample ?-z-test, with significance level of ?=0.05α=0.05, to test the null hypothesis, ?0:?=6.60 daysH0:μ=6.60 days, against the alternative hypothesis, ?1:?<6.60 days.H1:μ<6.60 days. The variable ?μ is the mean amount of time, in days, that it takes for customers to watch the first season of a television series. Scarlett selects a simple random sample of 740 customers who watched the first season of a television series from the company database of over 25,000 customers that qualified. She compiles the…

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