Do men take less time than women to get out of bed in the morning? The 48 men observed averaged 7.7 minutes to get out of bed after the alarm rang. Their standard deviation was 1.8. The 55 women...

Do men take less time than women to get out of bed in the morning? The 48 men observed averaged 7.7 minutes to get out of bed after the alarm rang. Their standard deviation was 1.8. The 55 women observed averaged 8 minutes and their standard deviation was 1.9 minutes. What can be concluded at the αα = 0.01 level of significance?

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


2. The null and alternative hypotheses would be:

 H0:H0:  Select an answer μ1 p1  Select an answer > ≠ = <  select an="" answer p2 μ2  (please="" enter="" a="">

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

1. The test statistic ? t z  =  (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 reject fail to 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 time for men to get out of bed in the morning is less than the population mean time for women to get out of bed in the morning.
   
   
   • The results are statistically insignificant at αα = 0.01, so there is statistically significant evidence to conclude that the population mean time for men to get out of bed in the morning is equal to the population mean time for women to get out of bed in the morning.
   
   
   • The results are statistically significant at αα = 0.01, so there is sufficient evidence to conclude that the mean time to get out of bed in the morning for the 48 men that were observed is less than the mean time for the 55 women that were observed.
   
   
   • The results are statistically insignificant at αα = 0.01, so there is insufficient evidence to conclude that the population mean time for men to get out of bed in the morning is less than the population mean time for women to get out of bed in the morning.
   
   

   
   
   
   


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

   
   
   • If the sample mean time to get out of bed for the 55 men is the same as the sample mean time to get out of bed for the 55 women and if another 48 men and 55 women are observed then there would be a 20.65% chance of concluding that the mean time to get out of bed for the 48 men is at least 0.3 minutes less than the mean time to get out of bed for the 55 women
   
   
   • There is a 20.65% chance that the mean time to get out of bed for the 48 men is at least 0.3 minutes less than the mean time to get out of bed for the 55 women.
   
   
   • There is a 20.65% chance of a Type I error.
   
   
   • If the population mean time for men to get out of bed in the morning is the same as the population mean time for women to get out of bed in the morning and if another 48 men and 55 women are observed then there would be a 20.65% chance that the mean time to get out of bed for the 48 men would be at least 0.3 minutes less than the mean time to get out of bed for the 55 women.
   
   

   
   
   
   


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

   
   
   • There is a 1% chance that there is a difference in the population mean time for men and women to get out of bed in the morning.
   
   
   • There is a 1% chance you will take so long to get out of bed in the morning that you will miss the deadline to complete this assignment.
   
   
   • If the population mean time for men to get out of bed in the morning is the same as the population mean time for women to get out of bed in the morning and if another 48 men and 55 women are observed then there would be a 1% chance that we would end up falsely concluding that the population mean time for men to get out of bed in the morning is less than the population mean time for women to get out of bed in the morning
   
   
   • If the population mean time for men to get out of bed in the morning is the same as the population mean time for women to get out of bed in the morning and if another 48 men and 55 women are observed then there would be a 1% chance that we would end up falsely concluding that the sample mean time for these 48 men and 55 women to get out of bed in the morning differ from each other.