Is memory ability before a meal better than after a meal? Ten people were given memory tests before their meal and then again after their meal. The data is shown below. A higher score indicates a...

Is memory ability before a meal better than after a meal?  Ten people were given memory tests before their meal and then again after their meal. The data is shown below. A higher score indicates a better memory ability.

Score on the Memory Test

Assume a Normal distribution.  What can be concluded at the the αα = 0.01 level of significance?

For this study, we should use Select an answer t-test for a population mean t-test for the difference between two dependent population means z-test for the difference between two population proportions t-test for the difference between two independent population means z-test for a population proportion

1. The null and alternative hypotheses would be:

 H0:H0:  Select an answer p1 μ1 μd  Select an answer < ≠ = >  Select an answer p2 0 μ2  (please enter a decimal)

 H1:H1:  Select an answer μd p1 μ1  Select an answer > < = ≠  select an="" answer p2 μ2 0  (please="" enter="" a="">

1. The test statistic ? z t  =  (please show your answer to 3 decimal places.)


2. The p-value =  (Please show your answer to 4 decimal places.)


3. The p-value is ? > ≤  αα


4. Based on this, we should Select an answer accept fail to reject reject  the null hypothesis.


5. Thus, the final conclusion is that ...
   
   
   

   
   
   • The results are statistically significant at αα = 0.01, so there is sufficient evidence to conclude that the population mean memory score before a meal is higher than the population mean memory score after a meal
   
   
   • The results are statistically insignificant at αα = 0.01, so there is statistically significant evidence to conclude that the population mean memory score before a meal is equal to the population mean memory score after a meal.
   
   
   • The results are statistically significant at αα = 0.01, so there is sufficient evidence to conclude that the ten memory scores from the memory tests that were taken before a meal are higher on average than the ten memory scores from the memory tests that were taken after a meal.
   
   
   • The results are statistically insignificant at αα = 0.01, so there is insufficient evidence to conclude that the population mean memory score before a meal is higher than the population mean memory score after a meal.
   
   

   
   
   
   


6. Interpret the p-value in the context of the study.
   
   
   

   
   
   • If the sample mean memory score for the 10 people who took the test before a meal is the same as the sample mean memory score for the 10 people who took the test after a meal and if another 10 people are given a memory test before and after a meal then there would be a 7% chance of concluding that the mean memory score for the 10 people who took the test before a meal is at least 3.3 points higher than the mean memory score for the 10 people who took the test after a meal.
   
   
   • There is a 7% chance of a Type I error.
   
   
   • If the population mean memory score before a meal is the same as the population mean memory score after a meal and if another 10 people are given a memory test before and after a meal then there would be a 7% chance that the mean memory score for the 10 people who took the test before a meal would be at least 3.3 points higher than the mean memory score for the 10 people who took the test after a meal.
   
   
   • There is a 7% chance that the mean memory score for the 10 people who took the test before a meal is at least 3.3 points higher than the mean memory score for the 10 people who took the test after a meal.
   
   

   
   
   
   


7. Interpret the level of significance in the context of the study.
   
   
   

   
   
   • There is a 1% chance that the population mean memory score is the same before and after a meal.
   
   
   • There is a 1% chance that your memory is so bad that you have already forgotten what this chapter is about.
   
   
   • If the population mean memory score before a meal is the same as the population mean memory score after a meal and if another 10 people are given a memory test before and after a meal, then there would be a 1% chance that we would end up falsely concuding that the sample mean memory scores before and after a meal for these 10 people who were part of the study differ from each other.
   
   
   • If the population mean memory score before a meal is the same as the population mean memory score after a meal and if another 10 people are given a memory test before and after a meal, then there would be a 1% chance that we would end up falsely concuding that the population mean memory score before a meal is higher than the population mean memory score after a meal