An article on the internet describes how people 15 to 19 years of age rarely read anymore. In particular, the article claims that people in this demographic read 10 minutes a day. The standard deviation of the amount of time people in the demographic read is known to be 5.8 minutes. However, you believe that this number is too low. In particular, you believe that people between 15 and 19 years of age read more than 10 minutes a day, which you set out to prove. You randomly sample 24 people between 15 and 19 years of age and find that they read for an average of 8 minutes with a standard deviation of 4.5 minutes. You may assume that the number of minutes spent reading within this demographic is approximately normally distributed.

What is the alternative hypothesis for this test?

Question

An article on the internet describes how people 15 to 19 years of age rarely read anymore. In particular, the article claims that people in this demographic read 10 minutes a day. The standard deviation of the amount of time people in the demographic read is known to be 5.8 minutes. However, you believe that this number is too low. In particular, you believe that people between 15 and 19 years of age read more than 10 minutes a day, which you set out to prove. You randomly sample 24 people between 15 and 19 years of age and find that they read for an average of 8 minutes with a standard deviation of 4.5 minutes. You may assume that the number of minutes spent reading within this demographic is approximately normally distributed.

What is the alternative hypothesis for this test?

BlackTom AI · Accepted Answer

The question asks for the alternative hypothesis in a test about the population mean μ of minutes read per day for 15- to 19-year-olds. Option 1: μ = 10. This is a statement of the null hypothesis (the value we test against), not the alternative. It asserts no difference from 10 minutes. Option 2: None of the other options are correct. This is a distractor; we can evaluate each option to see what they represent. Option 3: x̄ = 8. This is about the sample mean, not the population mean. It is a data result, not a hypothesis about μ. Option 4: x̄ = 10. Similar to Option 3, this describes the sample statistic, not the population parameter; it does not state a hypothesis about μ. Option 5: μ = 8. This is a specific claim about the population mean being 8 minutes, which is not what we are testing here given the belief is that the mean exceeds 10. Option 6: x̄ < 8. This is a statement about the sample mean, not a hypothesis about μ, and it also asserts a value (less than 8) rather than a direction about μ. Option 7: μ > 10. This is a directional claim about the population mean being greater than 10 minutes, which matches the belief you want to test and constitutes the alternative hypothesis in a one-sided test. Option 8: x̄ > 10. This asserts the sample mean exceeds 10, which is an observed statistic and not a population-parameter hypothesis; it could be a basis for a test decision, but it is not the formal alternative hypothesis. Option 9: μ < 8. This is a specific mean claim in the opposite direction and does not reflect the stated belief that the mean is over 10 minutes. In summary, the only option that correctly expresses the alternative hypothesis about the population mean in the stated direction is μ > 10, while the others either state the null, reference the sample statistic, or assert incorrect or irrelevant mean values or directions.

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