Question

In: Statistics and Probability

A researcher calculated average sleep hours per night for a random sample of (n= 4646) students....

A researcher calculated average sleep hours per night for a random sample of (n= 4646) students. The researcher hypothesised that a healthy person is expected to sleep 88 hours per night (μ0=8μ0=8). The sample mean y¯y¯ is equal to 7.97.9 hours and the sample variance s2n−1sn−12 is equal to 1.241.24 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: a one-sample t-test or a 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 Answer: true or false

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

Solutions

Expert Solution

The null and alternative hypothesis

8

8

This is a two tailed test ( as alternative hypothesis shows average sleep hours different from 8 , it does not show any direction , such as less than or more than 8 )

1) The most appropriate test for the data is : a one sample t test .

(Note : as we are testing about a population mean based on a sample , we are not comparing two or more samples , this is one sample t test )

2) Test statistic

  

= - 0. 61

Answer : Absolute value of test statistic = 0.61

Note : ( hypothesizd mean ) , s2= 1.24 , s= 1.1136 , n= 46

3) The degrees of freedom = n-1 = 46-1 =45

4) P value =0.5449

P value > 0.05

Answer : TRUE

Note : The excel formula for P value "=T.DIST.2T(0.61, 45)"

5) As P value > 0.05

The result is not significant

There is not sufficient evidence to conclude that average sleep hours is different from the hypothesized sleep hours.

Answer : The test shows that the average hours of sleep was equal to hypothesized hours of sleep per night.

orchestra answered 1 year ago
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