A group of students estimated the length of one minute without reference to a watch or clock, and the times (seconds) are listed below. Use a 0.01 significance level to test the claim that these times are from a population with a mean equal to 60 seconds. Does it appear that students are reasonably good at estimating one minute?

Complete Question

The complete question is shown on the first uploaded image  

Yes the students are reasonably good at estimating one minute

a

  Option A is  correct

b

  The test statistics is  

Step-by-step explanation:

From the question we are told that

    The  set of data is  

               68, 82 ,  38 ,  62 , 41, 25 , 57 ,  64, 67, 47, 61, 71, 91, 87, 64

     The  population mean is  

The  level of significance is given as

    The  critical value for this level of significance obtained from the normal distribution table is  

   The  null hypothesis is  

   The alternative hypothesis is  

Generally the sample mean is mathematically represented as

where  n = 15

 So  

The standard deviation is mathematically represented as

substituting values

                =>  

The  test statistics is evaluated as  

substituting values

Now comparing the statistics and the critical value of the level of significance we see that the the test statistics is less than the critical value

Hence the we fail to reject the null hypothesis which mean that these times are from a population with a mean equal to 60 seconds

So we can state that yes the students are reasonably good at estimating one minute given that the sample mean is not far from the population mean

b is 38 degrees.

a is 52 degrees.

this is because if b is 38 and a is 14 degrees more than b than 38+14=52 and 52+38=90 degrees. hope this .