Homework 4: Inferential Statistics
1. State the appropriate null and alternative hypothesis in each of the following cases:
a. The Battalion recently changed the format of their opinion page, you want to see what the students think of this change. You take a random sample of students and select those who regularly read the Battalion. They are asked to indicate their opinions on the changes using a 5-point scale. -2 if the new format is much worse than the old, -1 if the new format is worse than the old, 0 if the old format is the same as the old, 1 if the new format is better than the old and 2 if the new format is much better than the old.
b. The average square footage of one bedroom apartments in a new student housing development is advertised to be 880 square feet. A student group thinks that the apartments are smaller than advertised. They hire an engineer to measure a sample of apartments to test their suspicion.
c. The diameter of a spindle in a small motor is supposed to be 5 mm. If the spindle is either too small or too large, the motor will not work properly. The manufacturer measures the diameter in a sample of motors to determine whether the mean diameter has moved away from the target.
d. Census Bureau data show that the mean household income in the area served by a shopping mall is $42,500 per year. A market research firm questions shoppers at the mall. The researchers suspect the mean household income of mall shoppers is higher than that of the general population.
2. A vocabulary test is known to have a mean score of 68 and a standard deviation of 13. A class of 19 students takes the test and has a mean score of 65. (Use the appropriate test to check if the class score is really different.)
3. In the population, the average IQ is 100. A team of scientists want to test a new medication to check if it has positive or negative impact on intelligence, or no effect at all. A sample of 30 participants who have taken the medication has a mean of 140 with standard deviation of 20. Did medication affect intelligence?
4. A sample of size n = 100 produced the sample mean of X¯ = 16. Assuming the population standard deviation σ = 3, compute a 95% confidence interval for the population mean µ.
5. The operations manager of a large production plant would like to estimate the mean amount of time a worker takes to assemble a new electronic component. Assume that the standard deviation of this assembly time is 3.6 minutes.
a. After observing 120 workers assembling similar devices, the manager noticed that their average time was 16.2 minutes. Construct a 92% confidence interval for the mean assembly time.
b. How many workers should be involved in this study in order to have the mean assembly time estimated up to ±15 seconds with 92% confidence?
6. You work for a consumer advocate agency and want to find the mean repair cost of a certain brand of washing machine. As part of your study, you randomly select 40 repairs, determine their costs, and find the mean to be $100.00 with a standard deviation of $17.50.
a. Construct a 90% confidence interval for the mean repair cost. (Include all three steps:
check conditions, calculate the CI, and interpret it in context.)
b. Construct a 95% confidence interval. (You don’t need to check the conditions again, but calculate the CI and interpret it in context).
c. Construct a 99% confidence interval. (Again interpret it in context).