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 F.What does your decision mean?

You are a teacher at a gifted school, and you feel that the newest class of students is even brighter than usual. The mean IQ at your school is 127, and the mean IQ of this new class is 134. In total, there are 32 students in this new class. Also, the standard deviation of the school’s IQ is 8. Use the eight steps to test whether this new class of students is significantly more intelligent than the school’s student body overall.

Suppose that you randomly survey death records for people born in 1900 in Louisiana and compared the life span of two different ethnicities. Of the 109 individuals sampled from ethnicity 1, the mean life span was 45.5 years with a standard deviation of 18.2 years. Of the 105 individuals sampled from ethnicity 2, the mean life span was 44.9 years with a standard deviation of 11.4 years. Conduct a hypothesis test with a 10% level of significance to see if the mean life spans in Louisiana were the same for the two ethnicities. Step 1: State the null and alternative hypotheses. Ho: µ1 – µ2 =v Ha:H1 – µ2 # v (So we will be performing a two-tailed ♥ test.)

Suppose you've just been hired as a statistics professor, but you've never taught undergrads before. While you're doing your best, you're not sure you're fully up to par with all the other excellent statistics professors out there. You decide to look at your 41 students' grades on their midterm exam. They averaged grades of 81 on this exam, with a standard deviation of 10. You reason that if they're higher than normal, you might be making things too easy for them. Likewise, if they're lower than normal, you might be making things too hard. Seeking a Goldilocks effect, you compare this with the national average of statistics midterm exam scores - this is 79.  BEING SPECIFIC, what kind of statistical analysis should you perform, and WHY? Three parts of your answer will factor into the grade on this answer: the type of statistical test, one specific aspect of this test (hint- see the earlier questions), and your explanation as to why.

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In a school district, all sixth grade students take the same standardized test. The superintendant of the school district takes a random sample of 30 scores from all of the students who took the test. She sees that the mean score is 169 with a standard deviation of 7.0674. The superintendant wants to know if the standard deviation has changed this year. Previously, the population standard deviation was 13. Is there evidence that the standard deviation of test scores has decreased at the α=0.005 level? Assume the population is normally distributed. Step 4: Make a decision. Is it reject Null hypothesis or Fail to reject Null hypothesis? Step 5: What is the conclusion? Is there sufficient evidence or there is not sufficient evidence to show that the standard deviation of the test scores has decreased?

In preparation for the upcoming school year, a teacher looks at raw test scores on the statewide standardized test for the students in her class. Instead of looking at the scores relative to the norms in the state, the teacher wants to understand the scores relative to the students who will be in the class. To do so, she decides to convert the test scores into z-scores relative to the mean and standard deviation of the students in the class. The mean test score in her upcoming class is 49, and the standard deviation is 20.7. The teacher now wants to identify those students who may need extra help. She decides to look at students who have z-scores below z = -2.00 Identify the test score corresponding to a z-score of below z = -2.00. Round to the nearest whole number.

Russell is doing some research before buying his first house. He is looking at two different areas of the city, and he wants to know if there is a significant difference between the mean prices of homes in the two areas. For the 39 homes he samples in the first area, the mean home price is $⁢176,400. Public records indicate that home prices in the first area have a population standard deviation of $⁢32,930. For the 32 homes he samples in the second area, the mean home price is $⁢181,500. Again, public records show that home prices in the second area have a population standard deviation of $⁢23,835. Let Population 1 be homes in the first area and Population 2 be homes in the second area. Construct a 95% confidence interval for the true difference between the mean home prices in the two areas. Round the endpoints of the interval to the nearest whole number, if necessary. Lowest Endpoint =  upper Endpoint=

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:

An IQ test has a mean of 96 and a standard deviation of 15. Which is more​ unusual, an IQ of 81 or an IQ of 120​?