Question

Questions points Answer the following questions: An entrepreneurial scientist has invented a supplement that she believes can enhance short-term memory. She conducts an experiment to test the effect of the supplement on 23 volunteers, 12 of whom are given a placebo and 11 of whom are given the supplement. In analyzing in her study, she obtains a p-value of 0.19. Which of the following is a reasonable interpretation of her results This proves that at most 19% of the time, the experimental treatment has no effect on memory This proves that at least 19% of the time, the experimental treatment has no effect on memory She should fail to reject the null hypothesis She should reject the null hypothesis. Prairie Craft Brewery has an automated filling machine that is set to fill each bottle with 330 millilitres of the its new Redhead Rye Ale. They have just completed the testing on a sample of 100 bottles to to see if the machine is filling the bottles with an average of 330 mililitres of ale. The tester has obtained a mean of 339 ml and p-value of 0.005 for a right-tal test. Which definition of the p-value is the most accurate? Ris the probability of observing a mean of 339 or more under the assumption that the null hypothesis is true. It is the probability that the null hypothesis is true R is the probability that the observed mean of 339ml will occur again. It is the value that any sample mean must reach in order to be considered significant under the null hypothesis. - Food inspectors inspect samples of Alberta beef to see if they are safe. This can be thought of as a hypothesis test where Ho: the beef is safe Hy: the beef is not safe. At one plant, the inspector concludes the beet is safe when it actually is not safe. Which of the following statements is correct? The inspector has made a Type I error. The inspector has made a Type Il error is impossible to know which of the two types of error has been made without knowing the level of significance Ris impossible to know which of the two types of errors has been made without knowing the p-value a. It is reported that scores on a national accounting certification exam are approximately normally distributed with a mean of 84. 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 91. After conducting the appropriate statistical test, Professor Rose finds that the p-value is 0.0022 Which of the following is the best interpretation of the p-value? A p-value of 0.0022 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 0.0022 provides evidence that Professor Rose is an exceptional teacher who was able to prepare her students well for this exam. Ap-value of 0.0022 provides strong evidence that Professor Rose's class outperformed the other exam writers across the nation None of the above are reasonable interpretations of this result A human resources study claims that the average age of Canadians who retire is 65 years. You believe that the average age is less than that. You take a random sample of 452 Canadians who have retired, and find their average age to be 64.7 years, with a standard deviation of 2.10 years. Using the resulting p-value of 0.0012. you conclude that this is significantly lower than the age of 65 stated in the study. What would be the most appropriate interpretation of this result? Although the result is statistically significant the difference in age is of hele practical importance An error must have been made. This difference is too small to be statistically The statistically significant result indicates that the majority of people who retire are younger than 65 Without knowing the level of significance, it is impossible to know if the results are

Answer 1

(a) Answer is

She should fail to reject null hypothesis.

We reject the null hypothesis if p-value is less than the level of significance. In this case p-value is 0.19, usually the level of significance is 0.05 or 0.01 and p-value of 0.19 is very large than 0.05 or 0.01 so since p-value is greater than the level of significance hence she should fail to reject null hypothesis.

(b) Answer is

It is the probability of observing a mean of 339 ml or more under the assumption that the null hypothesis is true.

P-value is interpreted as the probability of observing an effect at least as extreme as the one in sample, under the assumption that the null hypothesis is true. Here the effect is mean and the sample mean is 339 hence the p-value is the probability of observing a mean of 339 ml or more under the assumption that the null hypothesis is true.

Please note that while calculating p-value we already assumption that the null hypothesis is true.

(c) Answer is

The inspector has made a Type II error.

Type II error occurs in situations where we accept the null hypothesis when in fact it is not true.

In this case inspector concludes that the beef is safe (that is he accepts null hypothesis) when it actually is not safe(when in fact null hypothesis is not true) which implies that the inspector accepts the null hypothesis when in fact it is not true which is the type II error.

Please note that it is possible to know which error has occurred without knowing level of significance and p-value.

(d) Answer is

A p-value of 0.0022 provides strong evidence that professor Rose's class outperformed the other exan writers across the nation.

We reject the null hypothesis if p-value is less than the level of significance. In this case p-value is 0.0022 and usually level of significance is 0.05 or 0.01 and here p-value of 0.0022 is very less than the level of significance 0.05 or 0.01 hence we reject the null hypothesis. Note that in this case

Ho: Test scores for professor Rose's students are not different from the national average score of 84.

Vs

H1: Test scores for professor Rose's students are higher than the national average score of 84.

Since p-value is very less than the level of significance of 0.05 or 0.01 we reject the null hypothesis. Hence the conclusion.

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