Question

In: Statistics and Probability

A researcher calculated average sleep hours per night for a random sample of (n= 5454) students....

A researcher calculated average sleep hours per night for a random sample of (n= 5454) students. The researcher hypothesised that a healthy person is expected to sleep 8.58.5 hours per night (μ0=8.5μ0=8.5). The sample mean y¯y¯ is equal to 8.28.2 hours and the sample variance s2n−1sn−12 is equal to 1.181.18 hours.

Research Question: Is the average hours of sleep equal to hypothesised hours of sleep per night?

Answer the following questions by choosing the most correct option or typing the answer:

  1. (1 mark) The most appropriate test for these data is: AnswerA one-sample t-testA two-sample t-test

For the remaining questions you may assume that any relevant assumptions have been met.

  1. The absolute value of the test statistic is equal to (type your answer with 3 dp) Answer

  2. (1 mark) The degrees of freedom is equal to (type your answer as an integer) Answer

  3. (1 mark) The p-value is larger than 0.05 Answertruefalse

  4. The test shows that the average hours of sleep was

Solutions

Expert Solution

one-sample t-test

..............

Ho :   µ =   8.5                  
Ha :   µ ╪   8.5       (Two tail test)          
                          
Level of Significance ,    α =    0.05                  
sample std dev ,    s =    1.0863                  
Sample Size ,   n =    54                  
Sample Mean,    x̅ =   8.2000                  
                             
                          
Standard Error , SE = s/√n =   1.0863   / √    54   =   0.1478      
t-test statistic= (x̅ - µ )/SE = (   8.200   -   8.5   ) /    0.1478   =   -2.029

The absolute value of the test statistic is equal to 2.029

.................

degree of freedom=   DF=n-1=   53                  
   ........................

p-Value   =   0.0474   [Excel formula =t.dist(t-stat,df) ]         

The p-value is larger than 0.05 false    


Decision:   p-value<α, Reject null hypothesis

..............

   The test shows that the average hours of sleep wAS not  equal to hypothesised hours of sleep per night

.......................

THANKS

revert back for doubt

please upvote

orchestra answered 1 year ago
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