You have been asked to determine if two midterm tests of the same class have different mean scores. Midterm test 1 has mean μ_{1} and midterm test 2 has mean μ_{2}. 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,
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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?
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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
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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
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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
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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 μ_{1} and midterm test 2 has mean μ_{2}. 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.  μ_{1}=μ_{2} 

B.  μ_{1}=0 

C.  μ_{2}=0 

D.  μ_{1}≠μ_{2} 
11.  In systematic random sampling, the researcher randomly selects
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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.
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A.  sample, population, sampling 

B.  sample, sampling, population 

C.  population, sample, sampling 

D.  sampling, sample, population 
According to the provided data, the sample mean and sample size for midterm 1 is 50 and 25 respectively. The sample mean and sample size for midterm 2 is 60 and 25 respectively. The test statistic is mentioned as 2.5.
The null and alternative hypotheses are;
The level of significance is 0.05 or 5%. The degrees of freedom, df = n1 +n2 – 2 = 25+25 – 2 = 48.
Using the tdistribution table, the tcriti...
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