Answer the following questions:
- Prairie Craft Brewery has an automated filling machine that is set to fill each bottle with 250 millilitres of the its new Redhead Rye Ale. They have just completed the testing on a sample of 70 bottles to to see if the machine is filling the bottles with an average of 250 millilitres of ale. The tester has obtained a mean of 260 ml and p-value of 0.001 for a right-tail test. Which definition of the p-value is the most accurate?
It is the probability that the observed mean of 260 ml will occur again. It is the probability that the null hypothesis is true. It is the probability of observing a mean of 260 ml or more under the assumption that the null hypothesis is true. It is the value that any sample mean must reach in order to be considered significant under the null hypothesis. - If a researcher was hoping to show that the results of an experiment were statistically significant which of the following would they prefer?
A small p-value A large p-value p-values are not related to statistical significance More information is required to correctly answer this question. - Food inspectors inspect samples of Alberta beef to see if they are safe. This can be thought of as a hypothesis test where
H0: the beef is safe
H1: the beef is not safe.
At one plant, the inspector concludes the beef is not safe when it actually is safe. Which of the following statements is correct?The inspector has made a Type I error. The inspector has made a Type II error. It is impossible to know which of the two types of errors has been made without knowing the level of significance. It is impossible to know which of the two types of errors has been made without knowing the p-value. - It is reported that scores on a national accounting certification exam are approximately normally distributed with a mean of 83. Professor Rose believes that students from her three sections of her preparatory course will score significantly higher than the national average on this test. After they write the exam, her students have scored an average of 89. After conducting the appropriate statistical test, Professor Rose finds that the p-value is 0.0017 Which of the following is the best interpretation of the p-value?
A p-value of 0.0017 provides strong evidence that Professor Rose's class outperformed the other exam writers across the nation. A p-value of 0.0017 indicates that there is a very small chance that Professor Rose's class outperformed the other exam writers across the nation. A p-value of 0.0017 provides evidence that Professor Rose is an exceptional teacher who was able to prepare her students well for this exam. None of the above are reasonable interpretations of this result. - A recent randomized poll of 150 Canadian adults concluded that 109 of those polled are, in principle, in favour of assisted dying legislation. A statistics student was going to use this sample information to conduct a Z-based test of significance of whether more than 95% of all Canadian adults agree with the legislation. What would you tell this student?
You need more information to assess the validity of a Z-based hypothesis test for this situation. The necessary conditions for a Z-based test of significance are not satisfied. The necessary conditions for a Z-based test of significance are satisfied. With such a large number of people favoring the legislation, there is no need for a statistical test. Question 2 [5 points]
A sample of size 169, taken from a population whose standard deviation is known to be 8.20, has a sample mean of 95.46. Suppose that we have adopted the null hypothesis that the actual population mean is greater than or equal to 96, that is, H0 is that μ ≥ 96 and we want to test the alternative hypothesis, H1, that μ < 96, with level of significance α = 0.01.a) What type of test would be appropriate in this situation? A right-tailed test. A left-tailed test. A two-tailed test None of the above.
b) What is the computed p-value?
For full marks your answer should be accurate to at least three decimal places.
p-value: 0c) Based on your p-value and the decision rule you have decided upon, what can we conclude about H0? There is sufficient evidence, at the given significance level, to reject H0. There is insufficient evidence, at the given significance level, to reject H0; or we fail to reject H0. There is insufficient evidence to make it clear as to whether we should reject or not reject the null hypothesis Question 3 [5 point
- A sample of size 23, taken from a population whose standard deviation is unknown, has a sample mean of 51.31 and a sample standard deviation of 7.40. Suppose that we have adopted the null hypothesis that the actual population mean is equal to 50, that is, H0 is that μ = 50 and we want to test the alternative hypothesis, H1, that μ ≠ 50, with level of significance α = 0.01.
a) What type of test would be appropriate in this situation? A right-tailed test. A left-tailed test. A two-tailed test None of the above.
b) What is the computed p-value?
For full marks your answer should be accurate to at least three decimal places.
This will require a statistical calculator or software package.
p-value: 0c) Based on your p-value and the decision rule you have decided upon, what can we conclude about H0? There is sufficient evidence, at the given significance level, to reject H0. There is insufficient evidence, at the given significance level, to reject H0; or we fail to reject H0. There is insufficient evidence to make it clear as to whether we should reject or not reject the null hypothesi