6. Interpreting conclusions of Hypothesis Tests. a) A television network has bel
ID: 3068825 • Letter: 6
Question
6. Interpreting conclusions of Hypothesis Tests. a) A television network has believed for many years that at least 40% of its viewers are below the age of 22. For marketing purposes, a potential advertiser wishes to test the claim that the percentage is actually less than 40%. After performing the test at the 0.05 level of significance, the advertiser decides to reject the null hypothesis. What does this conclusion lead us to believe about the potential advertiser's claim? b) A pharmaceutical company has publicized that no more than 4% ofpeople who take a particular drug experience significant side effects. A researcher is concerned that the percentage is more than 4%, and she decides to test her claim with a hypothesis test Based on the sample she collects, she decides to fail to reject the null hypothesis at the 0.01 level of significance. What does this conclusion tell us about the researcher's claim? c) A radio station has always believed that the mean age of its listeners is 26. Because their ratings are slipping, the executives need to know if the mean age has changed, so that they can alter their programs accordingly. After information is collected from 329 listeners and a hypothesis test is completed, the radio station executives decide that they should reject the null hypothesis with a 95% level of confidence. Based on this conclusion, should the radio station look into changing its programming?Explanation / Answer
6. a) Null Hypothesis = At least 40% of its viewer are below age 22
Alternative Hypothesis = Less than 40% of its viewer are below age 22
Interpretation: As the advertiser has decided to rejected the null hypothesis at 0.05 level of significance then that means that the advertiser claim is true. And less than 40% of its viewer are below age 22.
b) Null Hypothesis = No more than 4% experience significant side effects
Alternative Hypothesis = More than 4% experience significant side effects
Interpretation: As the researcher fail to reject the null hypothesis at 0.01 level of significance then that means that the researcher claim is false. And no more than 4% of people experience significant side effects.
c) Null Hypothesis = Mean age is 26
Alternative Hypothesis = Mean age is not 26
Interpretation: As the radio station executive decides to reject the null hypothesis at 0.05 level of significance then that means that the executive claim is true. The age of its listeners is not 26 and it has changed. So now they can alter the programs accordingly.
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