Question description

 

Do the following for each problem:

1. State Ho and Ha

2. Calculate z statistic (show all work)

3. Find p-value

4. Compare to significance level

5. State your conclusion (accept/reject)

 

1) The EPA reports that the exhaust emissions for a certain car model has a normal distribution with a mean of 1.45 grams of nitrous oxide per mile and a standard deviation of 0.4. The car manufacturer claims their new process reduces the mean level of exhaust emitted for this car model. A SRS of 28 cars is taken and the mean level of exhaust emitted for this sample is 1.21 grams. At the 1% level, can we state that the new process reduces the mean level of exhaust?

2) The amount of water consumed per week by Montana residences is normally distributed with an unknown mean μ and a standard deviation of 10 gallons. A simple random sample of ten residences has a mean value of x =120.3 gallons. The city of Bozeman claim that the average water consumed in the state of Montana is not 125 gallons. At the 10% significance level, can we accept the city's claim?

3) A credit card company wondered whether giving frequent flyer miles for every purchase would increase card usage, which has a current mean of $2500 per year. They gave free miles to a SRS of 51 credit card customers and found the sample mean to be $2542. Assume the population standard deviation is o = $109. At the 5% significance level, can we say that frequent flyer miles increased card usage?

4) Studies conducted in the 1970s indicated that the average age at which children went to the movies with their friends was 14.6 years old. Sociologists believe that children are going to the movies at an earlier age now. A SRS of 144 young adults (18 years of age) is selected and the age at which each adult went to their first movie with friends is recorded. The sample mean age was 13.3 years of age. The population standard deviation is known to be 5 years. At the 1% significance level, can we say that the mean age that a child went to the movies with their friends has changed?

 

5) Given here are the birth weights (in kg) of male babies born to mothers on a special vitamin supplement. The mean birth weight for all male babies is equal to 3.39 kg. Does the vitamin supplement appear to have an effect on birth weight? Assume that o = 0.66. Use a 5% significance. The weights of babies born to mothers on the supplement are : 3.73 4.37 3.73 4.33 3.39 3.68 4.68 3.52 3.02 4.09 2.47 4.13 4.47 3.22 3.43 2.54

6) Do male symphony conductors live longer, on average, than males in the general population? The mean life span for 35 male symphony conductors was 73.4 years, in contrast the mean of 69.5 years for males in the general population. Assuming that the 35 conductors is a random sample, and that o = 8.7 years, test the claim that the conductors have a longer average life span. Use a 10% significance level.

7) The effectiveness of a test preparation course was studied for a random sample of 75 students who took the SAT before and after coaching. The differences between the scores resulted in a mean increase of 0.6. At the 5% significance level, test the claim that the population mean increases is greater than 0, indicating that the course is effective in raising scores. Should people take this course? Assume that o = 3.8.