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Statistics Question-Linear

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.

Solution Preview

a) Write the null and alternative hypotheses to test the claim that the number of minutes spent online per day is related to gender.
Null hypothesis: Number of minutes spent online per day is not related to the gender
Alternative hypothesis: Number of minutes spent online per day is not related to the gender

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

Solution Summary

This solution states the null and alternative hypothesis, calculates the test statistic, compares it with p-value and makes a final decision in accepting or rejecting the null hypothesis.

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