Final answer:
The student's questions pertain to hypothesis testing in statistics, appropriate at the college level. They involve determining the correct test for a given scenario, setting up null and alternative hypotheses, and calculating degrees of freedom for a sample.
Step-by-step explanation:
The subjects addressed in the student's question revolve around concepts from statistics, which falls under the broader category of Mathematics. Specifically, they are related to hypothesis testing of a normal distribution. The student seems to be at the college level, given the complexity of the concepts and the language used. The questions cover topics such as constructing hypotheses, determining the appropriate test to use, understanding the significance level, and applying the correct distribution to analyze data.
For instance, in question 62, the appropriate test for the standard deviation greater than a certain value in a population would be the chi-square test for variance. In question 63, the null hypothesis could be that the population standard deviation is equal to 0.81, while the alternative hypothesis (Ha) would be that it is greater than 0.81. The df or degrees of freedom for this test, which is the solution to question 64, would be the sample size minus one, so here it would be 50 - 1 = 49.The question is asking about what type of test should be used when comparing the standard deviation of heights for the population to a given value.
In this case, the researcher believes that the standard deviation of heights for the school is greater than the given value of 0.81. To determine if this is true, a one-tailed hypothesis test should be used. The null hypothesis (H0) would state that the standard deviation of heights for the school is equal to or less than 0.81, while the alternative hypothesis (Ha) would state that the standard deviation is greater than 0.81.
The degrees of freedom (df) for the test can be calculated using the formula:
df = n - 1
Where n is the sample size. In this case, the sample size is given as 50, so the degrees of freedom would be 49.