You have been asked to determine if two midterm tests of the same class have different mean scores. Midterm test 1 has mean μ1 and midterm test 2 has mean μ2. Using a random sample of 25 students, the sample mean is 50 for midterm test 1 and 60 for midterm test 2. Test statistics is given and it equals to -2.5. At the 5% significance level, you would like to test whether the students have the same performance in the two midterm tests. What is the conclusion for this test? (4%) A. Reject the null hypothesis. B. Both the null hypothesis and alternative hypothesis are false. C. Reject the alternative hypothesis. D. Cannot reject the null hypothesis. 2. From a random sample of 300 students at a state university, you find the average number of hours of study time each week is 30 with a standard deviation of 5. In this research situation, (4%) A. the parameter is 5. B. the parameter is 30. C. the population is the 300 students surveyed. D. the sample is the 300 students surveyed. 3. A random sample of 100 students in a particular town was taken to estimate the mean monthly rent paid by the whole student population. The resulting The standard error of the mean is 4. Which of the following would decrease the standard error of the mean? (4%) A. An increase in sample size. B. An increase in population standard deviation C. An increase in sample mean. D. None of the above. 4. The Central Limit Theorem states that as sample size becomes large (4%) A. the population distribution becomes normal. B. the sampling distribution of sample means becomes normal. C. the sample distribution becomes normal. D. the sampling distribution of sample means becomes larger. 5. Cluster sampling often involves selecting (4%) A. cases alphabetically. B. systematic stratified clusters. C. geographical areas. D. older respondents only. 6. A professor claims that the average score on a recent exam was 84. Assume that the test scores are normally distributed. You believe that the average score is less than 84, therefore, you ask 9 people in class how they did, and you have the following information: sample mean = 80 and sample standard deviation (s) = 6. At the 5% significance level, you would like to test whether the professor’s statement was correct. What is the value of the test statistics for this test? (4%) A. 2 B. -1 C. 1 D. -2 7. A professor claims that the average score on a recent exam was 84. Assume that the test scores are normally distributed. You believe that the average score is less than 84, therefore, you ask 9 people in class how they did, and you have the following information: sample mean = 80 and sample standard deviation (s) = 6. At the 5% significance level, you would like to test whether the professor’s statement was correct. What is the number of degrees of freedom for this test? (4%) A. 8 B. 6 C. 9 D. 80 8. A professor claims that the average score on a recent exam was 84. Assume that the test scores are normally distributed. You believe that the average score is less than 84, therefore, you ask 9 people in class how they did, and you have the following information: sample mean = 80 and sample standard deviation (s) = 6. At the 5% significance level, you would like to test whether the professor’s statement was correct. What is the alternative hypothesis for this test? (4%) A. Average score > 84 B. Average score = 84 C. Average score < 84 D. None of the above 9. In a sampling distribution of sample means, most of the sample means will (4%) A. cluster around the true population value. B. be above the population mean in value. C. be below the population mean in value. D. not follow any particular pattern. 10. You have been asked to determine if two midterm tests of the same class have different mean scores. Midterm test 1 has mean μ1 and midterm test 2 has mean μ2. Using a random sample of 25 students, the sample mean is 50 for midterm test 1 and 60 for midterm test 2. Test statistics is given and it equals to -2.5. At the 5% significance level, you would like to test whether the students have the same performance in the two midterm tests. What is the null hypothesis for this test? (4%) A. μ1=μ2 B. μ1=0 C. μ2=0 D. μ1≠μ2 11. In systematic random sampling, the researcher randomly selects (4%) A. every other case. B. cases according to their scores. C. the first case and every kth case thereafter. D. cases following any systematic pattern. 12. The purpose of inferential statistics is to acquire knowledge of the _____ from the _____ by means of the _____ distribution. (4%) A. sample, population, sampling B. sample, sampling, population C. population, sample, sampling D. sampling, sample, population

You have been asked to determine if two midterm tests of the same class have different mean scores. Midterm test 1 has mean μ1 and midterm test 2 has mean μ2. Using a random sample of 25 students, the sample mean is 50 for midterm test 1 and 60 for midterm test 2. Test statistics is given and it equals to -2.5. At the 5% significance level, you would like to test whether the students have the same performance in the two midterm tests. What is the conclusion for this test? (4%) A. Reject the null hypothesis. B. Both the null hypothesis and alternative hypothesis are false. C. Reject the alternative hypothesis. D. Cannot reject the null hypothesis. 2. From a random sample of 300 students at a state university, you find the average number of hours of study time each week is 30 with a standard deviation of 5. In this research situation, (4%) A. the parameter is 5. B. the parameter is 30. C. the population is the 300 students surveyed. D. the sample is the 300 students surveyed. 3. A random sample of 100 students in a particular town was taken to estimate the mean monthly rent paid by the whole student population. The resulting The standard error of the mean is 4. Which of the following would decrease the standard error of the mean? (4%) A. An increase in sample size. B. An increase in population standard deviation C. An increase in sample mean. D. None of the above. 4. The Central Limit Theorem states that as sample size becomes large (4%) A. the population distribution becomes normal. B. the sampling distribution of sample means becomes normal. C. the sample distribution becomes normal. D. the sampling distribution of sample means becomes larger. 5. Cluster sampling often involves selecting (4%) A. cases alphabetically. B. systematic stratified clusters. C. geographical areas. D. older respondents only. 6. A professor claims that the average score on a recent exam was 84. Assume that the test scores are normally distributed. You believe that the average score is less than 84, therefore, you ask 9 people in class how they did, and you have the following information: sample mean = 80 and sample standard deviation (s) = 6. At the 5% significance level, you would like to test whether the professor’s statement was correct. What is the value of the test statistics for this test? (4%) A. 2 B. -1 C. 1 D. -2 7. A professor claims that the average score on a recent exam was 84. Assume that the test scores are normally distributed. You believe that the average score is less than 84, therefore, you ask 9 people in class how they did, and you have the following information: sample mean = 80 and sample standard deviation (s) = 6. At the 5% significance level, you would like to test whether the professor’s statement was correct. What is the number of degrees of freedom for this test? (4%) A. 8 B. 6 C. 9 D. 80 8. A professor claims that the average score on a recent exam was 84. Assume that the test scores are normally distributed. You believe that the average score is less than 84, therefore, you ask 9 people in class how they did, and you have the following information: sample mean = 80 and sample standard deviation (s) = 6. At the 5% significance level, you would like to test whether the professor’s statement was correct. What is the alternative hypothesis for this test? (4%) A. Average score > 84 B. Average score = 84 C. Average score < 84 D. None of the above 9. In a sampling distribution of sample means, most of the sample means will (4%) A. cluster around the true population value. B. be above the population mean in value. C. be below the population mean in value. D. not follow any particular pattern. 10. You have been asked to determine if two midterm tests of the same class have different mean scores. Midterm test 1 has mean μ1 and midterm test 2 has mean μ2. Using a random sample of 25 students, the sample mean is 50 for midterm test 1 and 60 for midterm test 2. Test statistics is given and it equals to -2.5. At the 5% significance level, you would like to test whether the students have the same performance in the two midterm tests. What is the null hypothesis for this test? (4%) A. μ1=μ2 B. μ1=0 C. μ2=0 D. μ1≠μ2 11. In systematic random sampling, the researcher randomly selects (4%) A. every other case. B. cases according to their scores. C. the first case and every kth case thereafter. D. cases following any systematic pattern. 12. The purpose of inferential statistics is to acquire knowledge of the ___ from the _ by means of the ___ distribution. (4%) A. sample, population, sampling B. sample, sampling, population C. population, sample, sampling D. sampling, sample, population

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Description: You have been asked to determine if two midterm tests of the same class have different mean scores. Midterm test 1 has mean μ1 and midterm test 2 has mean μ2. Using a random sample of 25 students, the sample mean is 50 for midterm test 1 and 60 for m

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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You have been asked to determine if two midterm tests of the same class have different mean scores. Midterm test 1 has mean μ₁ and midterm test 2 has mean μ₂. Using a random sample of 25 students, the sample mean is 50 for midterm test 1 and 60 for midterm test 2. Test statistics is given and it equals to -2.5. At the 5% significance level, you would like to test whether the students have the same performance in the two midterm tests. What is the conclusion for this test? (4%)
	A.	Reject the null hypothesis.
	B.	Both the null hypothesis and alternative hypothesis are false.
	C.	Reject the alternative hypothesis.
	D.	Cannot reject the null hypothesis.

2.	From a random sample of 300 students at a state university, you find the average number of hours of study time each week is 30 with a standard deviation of 5. In this research situation, (4%)
	A.	the parameter is 5.
	B.	the parameter is 30.
	C.	the population is the 300 students surveyed.
	D.	the sample is the 300 students surveyed.

3.	A random sample of 100 students in a particular town was taken to estimate the mean monthly rent paid by the whole student population. The resulting The standard error of the mean is 4. Which of the following would decrease the standard error of the mean? (4%)
	A.	An increase in sample size.
	B.	An increase in population standard deviation
	C.	An increase in sample mean.
	D.	None of the above.

4.	The Central Limit Theorem states that as sample size becomes large (4%)
	A.	the population distribution becomes normal.
	B.	the sampling distribution of sample means becomes normal.
	C.	the sample distribution becomes normal.
	D.	the sampling distribution of sample means becomes larger.

5.	Cluster sampling often involves selecting (4%)
	A.	cases alphabetically.
	B.	systematic stratified clusters.
	C.	geographical areas.
	D.	older respondents only.

6.	A professor claims that the average score on a recent exam was 84. Assume that the test scores are normally distributed. You believe that the average score is less than 84, therefore, you ask 9 people in class how they did, and you have the following information: sample mean = 80 and sample standard deviation (s) = 6. At the 5% significance level, you would like to test whether the professor’s statement was correct. What is the value of the test statistics for this test? (4%)
	A.	2
	B.	-1
	C.	1
	D.	-2

7.	A professor claims that the average score on a recent exam was 84. Assume that the test scores are normally distributed. You believe that the average score is less than 84, therefore, you ask 9 people in class how they did, and you have the following information: sample mean = 80 and sample standard deviation (s) = 6. At the 5% significance level, you would like to test whether the professor’s statement was correct. What is the number of degrees of freedom for this test? (4%)
	A.	8
	B.	6
	C.	9
	D.	80

8.	A professor claims that the average score on a recent exam was 84. Assume that the test scores are normally distributed. You believe that the average score is less than 84, therefore, you ask 9 people in class how they did, and you have the following information: sample mean = 80 and sample standard deviation (s) = 6. At the 5% significance level, you would like to test whether the professor’s statement was correct. What is the alternative hypothesis for this test? (4%)
	A.	Average score > 84
	B.	Average score = 84
	C.	Average score < 84
	D.	None of the above

9.	In a sampling distribution of sample means, most of the sample means will (4%)
	A.	cluster around the true population value.
	B.	be above the population mean in value.
	C.	be below the population mean in value.
	D.	not follow any particular pattern.

10.	You have been asked to determine if two midterm tests of the same class have different mean scores. Midterm test 1 has mean μ₁ and midterm test 2 has mean μ₂. Using a random sample of 25 students, the sample mean is 50 for midterm test 1 and 60 for midterm test 2. Test statistics is given and it equals to -2.5. At the 5% significance level, you would like to test whether the students have the same performance in the two midterm tests. What is the null hypothesis for this test? (4%)
	A.	μ₁=μ₂
	B.	μ₁=0
	C.	μ₂=0
	D.	μ₁≠μ₂

11.	In systematic random sampling, the researcher randomly selects (4%)
	A.	every other case.
	B.	cases according to their scores.
	C.	the first case and every k^th case thereafter.
	D.	cases following any systematic pattern.

12.	The purpose of inferential statistics is to acquire knowledge of the _____ from the _____ by means of the _____ distribution. (4%)
	A.	sample, population, sampling
	B.	sample, sampling, population
	C.	population, sample, sampling
	D.	sampling, sample, population

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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