Question

A researcher calculated average sleep hours per night for a random sample of (n= 5959) students. The researcher hypothesised that a healthy person is expected to sleep 7.57.5 hours per night (?0=7.5μ0=7.5). The sample mean ?¯y¯ is equal to 88 hours and the sample variance ?2?−1sn−12is equal to 1.171.17 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.

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

5. (1 mark) The degrees of freedom is equal to (type your answer as an integer)  Answer

6. (1 mark) The p-value is larger than 0.05 Answertruefalse

7. The test shows that the average hours of sleep was Answersignificantly different than hypothesised value (lower).significantly different than hypothesised value (greater).not significantly different then the hypothesised value.

Answer 1

1) one sample t test

2)

Ho :   µ =   7.5
Ha :   µ ╪   7.5
      
Level of Significance ,    α =    0.050
sample std dev ,    s =    1.0817
Sample Size ,   n =    59
Sample Mean,    x̅ =   88.0000
      
degree of freedom=   DF=n-1=   58
      
Standard Error , SE = s/√n =   1.0817/√59=   0.1408
t-test statistic= (x̅ - µ )/SE =    (88-7.5)/0.1408=   571.648

3) degree of freedom=   DF=n-1=   58

4) False

5)

The test shows that the average hours of sleep was Answersignificantly different than hypothesised value

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