Problem 80

Given information

At Rachel’s  birthday party, eight girls were timed to see how long (in seconds) they could hold their breath in a relaxed position. After a two-minute rest, they timed themselves while jumping. The girls thought that the mean difference between their jumping and relaxed times would be zero.

Step-by-step explanation

According to the instructions in the problem, Eight girls were timed during Rachel's birthday party to test how long they could hold their breath in a relaxed position (in seconds). They timed themselves while jumping after a two-minute break. The girls assumed there would be no difference between their jumping and relaxed times.

Now, consider the tables given to arrive at the following observations:

The null hypothesis is defined as follows:

 

The alternative hypothesis is stated as follows:

 

The average difference between jumping and relaxed timings is the random variable .

We employ a -degree-of-freedom student's t distribution.

For the mean difference, the paired test static is,

After ENTE all of the values, look at the OUTPUT below,

Test statistic is  

  The   from the output is .

Drawing a representation of the situation using the information from the last exercise.

The horizontal axis should be clearly labeled and scaled, and the region(s) matching the should be shaded on the graph.

    

  

     

   Decision: Null hypothesis is rejected.

   

  Conclusion: There is insufficient evidence to establish that the average difference is not zero at the 5% level of significance.

Therefore, it is concluded that there is insufficient evidence to conclude that the average difference is not zero.