Project #14683 - Hypotheses

 

1. According to a study conducted in 2000, residents of new york listen to an average of 3.1 hours of music per week. You want to conduct a 95% hypothesis test to see if that is still the case, so you sample 110 people and find a sample mean of 3.6 hours with a standard deviation of 1.1 hours. Conduct a two-tailed, 95% hypothesis test to see if the parameter (the average time new yorkers  spend listening to music in a week) really is 3.1.

            (a) What are your hypotheses and alpha?

 

            (b) What is the test statistic?

 

            (c) What is the p-value?

 

            (d) Report your results and conclusions.

 

2. You want to test if the dice at your local casino’s craps table are fair. Because the dice have six sides, you should expect that the probability any one side comes up on a roll of a fair die is 1/6, or about .167 (in other words, the proportion any one side of a die comes up out of all possible rolls—i.e. the population—is .167). To test whether the die is fair—whether the population proportion really is .167—you roll the die 500 times and record that 1 comes up 87 times for a sample proportion of .174. Perform a two-tailed, 95% hypothesis test to see if the die is fair.

 

 

 

            (a) What are your hypotheses and alpha?

 

            (b) What is the test statistic?

 

            (c) What is the p-value?

 

            (d) Report your results and conclusions.

 

 

 

3. According to the 2005 Temple University Student Handbook, the average distance of a Temple University student’s hometown away from North Philadelphia is 2 hours. You suspect that his average is higher today than it was in 2005, so you decide to perform a one-tailed, 95% hypothesis test to see if the parameter really is 2 hours. You sample 55 temple students and find that the average distance of their hometowns away from Temple (i.e. the sample mean) is 2.2 hours with a standard deviation of 1.1 hours. Perform this hypothesis test making sure to complete the four steps outlined above in problems 1 and 2.

 

 

 

4. A USA Today article from 2007 reported that 57% of college students in the United States were women. You believe that this gender gap is in fact wider today than it was then, meaning that you believe the proportion of female college students is in fact greater than .57. You decide to test whether or not that is the proportion of the population today, so you sample 1,500 college students and find that 880 are female. Perform a one-tailed, 95% hypothesis test that includes all four steps.

 

Subject Mathematics
Due By (Pacific Time) 10/15/2013 12:00 am
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