SOLUTION: For the following question, each part of the question is worth 8 points. A researcher wants to determine whether the number of minutes adults spend online per day is related to

Question 140651: For the following question, each part of the question is worth 8 points.
A researcher wants to determine whether the number of minutes adults spend online per day is related to gender. A random sample of 315 adults was selected and the results are shown below. Test the claim that the number of minutes spent online per day is related to gender. Use α=0.05.
Minutes Spent Online Per Day
Gender 0 � 30 30 � 60 60 � 90 90 or over
Male 25 35 75 45
Female 30 45 45 15

a) Write the null and alternative hypotheses to test the claim that the number of minutes spent online per day is related to gender.

b) Show how you would calculate the expected number of males to spend 60-90 minutes online. Do not carry out the calculations. However, show how you would calculate the expected value.

c) How many degrees of freedom should you use to determine the critical value? Explain how you arrived at that number of degrees of freedom.

d) Suppose that the value of the χ2 test statistic is 18.14 and suppose that the critical value is 7.815. What conclusion would draw about the null hypothesis? Explain what numbers you are comparing to decide whether to reject or fail to reject the null hypothesis.

e) State your conclusion in terms of the original claim and indicate why you are justified in making this conclusion.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A researcher wants to determine whether the number of minutes adults spend online per day is related to gender. A random sample of 315 adults was selected and the results are shown below. Test the claim that the number of minutes spent online per day is related to gender. Use α=0.05.
Minutes Spent Online Per Day
Gender 0 � 30 30 � 60 60 � 90 90 or over Totals
Male.... 25..... 35..... 75..... 45.........180
Female.. 30 .....45..... 45..... 15 ........135
Totals...55......80......120.....60.........315
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a) Write the null and alternative hypotheses to test the claim that the number of minutes spent online per day is related to gender.
Ho: minutes oand gender are independent
Ha: they are dependent
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b) Show how you would calculate the expected number of males to spend 60-90 minutes online. Do not carry out the calculations. However, show how you would calculate the expected value.
Expected (for the 75 box) = (180/315)(120) = 68.57..
Comment this is pn where p=(180/315) and n = 120
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Expected (for the 45 box) = (135/315)(120) = 51.43..
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c) How many degrees of freedom should you use to determine the critical value? Explain how you arrived at that number of degrees of freedom.
df = (# of rows -1)(# of columns -1) = (2-1)(4-1) = 1*3 = 3
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d) Suppose that the value of the χ2 test statistic is 18.14 and suppose that the critical value is 7.815. What conclusion would draw about the null hypothesis?
Reject Ho.
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Explain what numbers you are comparing to decide whether to reject or fail to reject the null hypothesis.
The test statistic is greater than the critical value so Reject Ho.
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e) State your conclusion in terms of the original claim and indicate why you are justified in making this conclusion.
The test does not support the claim that minutes and gender are independent.
Gender and minutes watching TV seem to be dependent.
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Cheers,
Stan H.

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