Elementary Statistics Week 07 Assignment
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.
The key steps to tests of significance are to state H0 and HA, calculate the test statistic, compute the pvalue, and make a conclusion based on the given significance level. If you input H0, HA, and the summary statistics into Minitab Express, Minitab Express will output the p-value and you will not have to make any complex calculations. Keep in mind that the results obtained from software are not meaningful unless the correct null and alternative hypotheses are determined.
Here is an example of what you will need to do for four of the six problems in this assignment:
Testing the Population Proportion
A noted psychic was tested for ESP. The psychic was presented with 200 cards face down and asked to determine if the card was one of five symbols: a star, cross, circle, square, or three wavy lines. The psychic correctly identified 50 cards. If the psychic is truly guessing the shape on the cards, the proportion of correct guesses would be 1/5 = 0.20. Does this experiment give enough evidence to suggest that the psychic has ESP? (Use a 1% significance level.)
WORK YOU NEED TO SUBMIT:
Solution Question 1:
Step 1: H0: p = 0.2
HA: p > 0.2
Step 2: z = 1.77
Step 3: p-value = 0.039
Step 4: Do not reject H0 at the 1% level. There is not enough evidence to suggest that the psychic has ESP. 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.
Step 2: Calculate the test statistic.
Step 3: Find the 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. A company hopes to improve customer satisfaction, setting a goal of no more than 5% negative comments. A random survey of 350 customers found only 14 with complaints. Does this provide evidence at the 10% significance level that the company has reached its goal of decreasing the percentage of complaints?
2. The Pew Internet and American Life Project reported Wednesday, April 18th that two-thirds (67%) of young adults with profiles on social-networking sites have restricted access to their profiles by requiring passwords or making them available only to friends on an approved list (“Study: Teens protecting their profiles”
POSTED: 10:54 a.m. EDT, April 19, 2007 on CNN.com). A researcher believes that military personnel are more careful with keeping themselves safe online and surveys a random sample of 100 enlisted military personnel students and finds that 78 students restrict access to their profiles. Does this indicate at the 5% significance level that a larger proportion of military personnel protect their profiles on social-networking sites?
3. The National Collegiate Athletic Association (NCAA) requires colleges to report the graduation rates of their athletes. Here are data from a Big Ten university's report. Ninety-five of the 147 athletes admitted in 1989- 1991 graduated within six years. Does this indicate at a 1% significance level that the proportion of athletes who graduate differ significantly from the all-university proportion, which was 70%?
4. In a survey of 284 smokers, 197 smokers reported that they wanted to quit smoking. Compute a 90% confidence interval for the true proportion of smokers that want to quit smoking. (Adapted from the American Lung Association)
5. Nicotine patches are often used to help smokers quit. Does giving medicine to fight depression help? A randomized double-blind experiment assigned 244 smokers who wanted to stop to receive nicotine patches and another 245 to receive both a patch and the antidepressant drug bupropion. After a year, 40 participants in the nicotine patch group and 87 in the patch-plus-drug group had abstained from smoking. Count that Abstained From Smoking Sample Size
Patch + bupropion 87 245
Patch Only 40 244
Is there a significantly higher proportion of the patients that receive the patch plus bupropion abstaining from smoking than the patch only group? Carry out a test of significance at the 5% significance level.
6. A random sample of individuals participating in a survey in 2000 was asked “Do you favor or oppose the death penalty for murder?” The results were 130 out of 200 females favored capital punishment and 188 out of 250 males favored capital punishment. Find an approximate 95% confidence interval for the difference between the proportion of females and males that favor capital punishment.
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