Assignment Guidelines:
o Your work must be organized neatly and typed.
o Clearly indicate your name and the assignment number in the file name.
o Electronic copies of your work can be submitted as an attachment to the drop box.
o You need to hand in individual work. You may talk with each other about the problems. However, everything in the assignment must be your own work.
o No late assignments will be accepted.
If the question requires a test of significance, your solution should clearly show the four steps to the test. In addition, you should show that you have checked that the conditions for inference are met.
Step 1: State the null and alternative hypothesis. (Use "mu" for the symbol μ.)
Step 2: Calculate the test statistic.
Step 3: Find p-value.
Step 4: State your conclusion. (Do not just say "Reject H0" or "Do not reject H0." State the conclusion in the context of the problem.)
1. In an advertisement, a pizza shop claims its mean delivery time is 30 minutes.
A consumer group believes that the mean delivery time is greater than the pizza shop claims.
A random sample of 41 delivery times has a mean of 31.5 minutes with standard deviation of 3.5 minutes.
Does this indicate at a 5% significance level that the mean delivery time is longer than what the pizza shop claims?
2. How much does the cholesterol-lowering drug Gemfibrozil help reduce the risk of heart attack?
We compare the risk of heart attack over a 5-year period for two independent groups of middle-aged men taking either the drug or a placebo.
Does this provide evidence at the 5% significance level that the drug helps reduce the risk of heart attack?
Heart Attack Sample Size
Drug 56 2051
Placebo 84 2030
3. In lobbying Congress for action to correct the ozone depletion problem, the environmental group Save Planet Earth claims that 70% of the population supports the ban on household aerosols.
In a survey by Media General and the Associated Press, 150 of the 200 respondents indicated support for a ban on household aerosols.
Test the claim, at the 1% significance level, that more than 70% of the population supports the ban on household aerosols.
4. Extreme cold and hot temperatures are known to affect the operation of electronic components.
Winter is approaching and you are interested in the mean minimum temperature that will damage an iPod.
As a research project, 9 iPods were tested to see what minimum temperature damaged the electronic component.
The damaging temperature averaged 5 ºF with a standard deviation of 3 ºF.
Find a 95% confidence interval for the true mean minimum temperature that will damage an iPod. (Disclaimer: Apple recommends that to "keep iPod comfy," the iPod's battery should be kept between temperatures of 32 ºF and 95 ºF.)
5. A music industry producer wondered whether there was a difference in length (measured in seconds) of rhythm and blues songs (R&B) songs versus alternative rock songs.
He obtained a random sample of songs from each music category and documented the song lengths.
The results are in the following table. Test at a 10% significance level whether the rhythm and blues songs are longer than alternative rock songs.
Mean (seconds) Standard Deviation (seconds) Sample Size
R & B 242.7 26.9 30
Alternative Rock 230.3 28.9 30