**Transcription:**---A college professor claims that the entering class this year appears to be smarter than entering classes from previous years. He tests a random sample of 17 of this year's entering students and finds that their mean IQ score is 121, with standard deviation of 11. The college records indicate that the mean IQ score for entering students from previous years is 115. If we assume that the IQ scores of this year's entering class are normally distributed, is there enough evidence to conclude, at the 0.05 level of significance, that the mean IQ score, μ, of this year's class is greater than that of previous years?Perform a one-tailed test. Then complete the parts below.Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)(a) State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \).\[ H_0 : \square \]\[ H_1 : \square \](b) Determine the type of test statistic to use.\[ \text{(Choose one)} \](c) Find the value of the test statistic. (Round to three or more decimal places.)\[ \square \](d) Find the critical value. (Round to three or more decimal places.)\[ \square \](e) Can we conclude, using the 0.05 level of significance, that the mean IQ score---**Explanation of Diagrams:**The image includes two sections for entering hypotheses and test statistics, which are likely to be filled out by students as part of their coursework. The mathematical symbols are part of an equation editor to assist in formulating hypotheses and calculations. There are no graphs or complex diagrams included. ## Hypothesis Testing ExercisePerform a one-tailed test. Then, complete the parts below.Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)### Instructions**(a)** State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \).- \( H_0: \) [ ]- \( H_1: \) [ ]**(b)** Determine the type of test statistic to use.- [Choose one]**(c)** Find the value of the test statistic. (Round to three or more decimal places.)- [ ]**(d)** Find the critical value. (Round to three or more decimal places.)- [ ]**(e)** Can we conclude, using the 0.05 level of significance, that the mean IQ score of this year's class is greater than that of previous years?- [ ] Yes- [ ] No### NotesA small blue box contains symbols such as:- \( \mu, \sigma, \rho, \alpha, \beta \)- Square root- Square and cube functions- Inequality symbolsYou should use these tools to fill in the blanks and solve the problem step by step.

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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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Scores on a statistics final in a large class were normally distributed with a mean of 75 and a standard deviation of 8. The instructor wants to give an A to the students whose scores were in the top 08% of the class (Provide your answer with two decimal places). Find the Z-score that is associated with the lowest possible score to get an A. What is the minimum score needed to get an A?
A professor believes the class he is teaching in the current semester is below the average of the classes he has taught. In order to test this hypothesis, he analyses the scores of midterm of all 100 students he teaches this semester. Their average score of this exam is 79 out of 100, with a standard deviation of 12. The mean score of the midterm for all students that he has taught for the last thirty-two years is 83 out of 100, with a standard deviation of 14. Use an alpha level of 0.01 for this analysis. Part B.State the null hypothesis and the alternative hypothesis:
Use z scores to compare the given values. The tallest living man at one time had a height of 238 cm. The shortest living man at that time had a height of 142.4 cm. Heights of men at that time had a mean of 175.45 cm and a standard deviation of 5.59 cm. Which of these two men had the height that was more extreme? ... Since the z score for the tallest man is z = 0 and the z score for the shortest man is z = the man had the height that was Im- more extreme. (Round to two decimal places.) shortest tallest
A statistics teacher taught a large introductory statistics class, with 500 students having enrolled over many years. The mean score over all those students on the first midterm was u = 88 with standard deviation o = 10. One year, the teacher taught a %3D much smaller class of only 25 students. The teacher wanted to know if teaching a smaller class was more effective and students performed better. We can consider the small class as an SRS of the students who took the large class over the years. The average midterm score was = 78. The hypothesis should be: a. Ho: H = 78 vs. Ha: H = 88. %3D O b. Ho: µ = 88 vs. Ha: µ 78 %3D Ο d. Ho: μ-88 νs. Ha: μ >88. %3D
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A psychologist obtains a random sample of 30 mothers in the first trimester of their pregnancy. The mothers are asked to play Mozart in the house at least 45 minutes each day until they give birth. We know that IQs are normally distributed with a mean of 100. A few years after their births the children were given an IQ test and the IQs of the 30 children in the study resulted in a sample mean of 104.2. Assume the population standard deviation for IQ of children is 15. Is there evidence that the children who listen to Mozart for at least 45 minutes each day during pregnancy have higher IQs at the 0.05 level of significance? Step 1: Define the parameter & setup the testStep 2: State the Level of SignificanceStep 3: Find the value of the Test StatisticsStep 4: Find P-Value OR Find Critical ValueStep 5: State Conclusion and why
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Pilots who cannot maintain regular sleep hours due to their work schedule often suffer from insomnia. A recent study on sleeping patterns of pilots focused on quantifying deviations from regular sleep hours. A random sample of 28 commercial airline pilots was interviewed, and the pilots in the sample reported the time at which they went to sleep on their most recent working day. The study gave the sample mean and standard deviation of the times reported by pilots, with these times measured in hours after midnight. (Thus, if the pilot reported going to sleep at p.m., the measurement was -1.) The sample mean was 0.8 hours, and the standard deviation was 1.6 hours. Assume that the sample is drawn from a normally distributed population. Find a 90% confidence interval for the population standard deviation, that is, the standard deviation of the time (hours after midnight) at which pilots go to sleep on their work days. Then give its lower limit and upper limit.
In a school district, all sixth grade students take the same standardized test. The superintendant of the school district takes a random sample of 3030 scores from all of the students who took the test. She sees that the mean score is 169169 with a standard deviation of 7.06747.0674. The superintendant wants to know if the standard deviation has changed this year. Previously, the population standard deviation was 1313. Is there evidence that the standard deviation of test scores has decreased at the α=0.005α=0.005 level? Assume the population is normally distributed. Step 1 of 5: State the null and alternative hypotheses. Round to four decimal places when necessary. Step 2 of 5: Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer to three decimal places. Step 3 of 5: Determine the value of the test statistic. Round your answer to three decimal places. Step 4 of 5: Make the…
In Professor Krugman’s economics course, the correlation between the students’ total scores prior to the final examination and their final‑examination scores is ?=0.5.r=0.5. The pre‑exam totals for all students in the course have mean 280280 and standard deviation 40.40. The final‑exam scores have mean 7575 and standard deviation 8.8. Professor Krugman has lost Julie’s ﬁnal exam but knows that her total before the exam was 300.300. He decides to predict her ﬁnal‑exam score from her pre‑exam total. (a) Which of the choices is the least‑squares regression line of ﬁnal‑exam scores on pre‑exam total scores in this course?
Suppose that you are designing an instrument panel for a large industrial machine. The machine requires the person using it to reach 2 feet from a particular position. The reach from this position for adult women is known to have a mean of 2.7 feet with a standard deviation of 0.5. The reach for adult men is known to have a mean of 3.1 feet with a standard deviation of 0.7. Both women's and men's reach from this position is normally distributed. If this design is implemented, (a) what percentage of women will not be able to work on this instrument panel? (b) What percentage of men will not be able to work on this instrument panel? (c) Explain your answers to a person who has never had a course in statistics. Click here to view page 1 of the table. Click here to view page 2 of the table. Click here to view page 3 of the table. Click here to view page 4 of the table.
A math teacher claims that she has developed a review course that increases the scores of students on the math portion of a college entrance exam. Based on data from the administrator of the exam, scores are normally distributed with μ = 514. The teacher obtains a random sample of 1800 students, puts them through the review class, and finds that the mean math score of the 1800 students is 520 with a standard deviation of 112. Complete parts (a) through (d) below. to = 1.04 (Round to two decimal places as needed.) Find the P-value. The P-value is (Round to three decimal places as needed.)

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