We Want To Estimate P, The Proportion Of The Population Who Believes The State Of The

1. We want to estimate p, the proportion of the population who believes the state of the economy is the most urgent national concern with 99% confidence, and a margin of error no larger than 2%.

How many people need to be surveyed?
Use a critical value with three decimal places of accuracy for this problem!

Sample size:

2. In 2006, Merck released a vaccine named Gardasil for HPV – the most common cause of cervical cancer among young women. The company conducted four placebo controlled double blind clinical studies of women aged 16 to 26. The results were

(a): Give a 98% confidence interval for the differences in the proportion of young women who develop cervical cancer with and without the vaccine.

Lower confidence level:

Upper confidence level:

(b): Give a 98% confidence interval for the differences in the proportion of young women who develop genital warts with and without the vaccine.

Lower confidence level:

Upper confidence level:

Note: your answers should have at least three significant figures.

3. Here is data on the age (in months) that 20 children said their first words of English.

If you treat this as an SRS, does it provide evidence at significance level 4% that the mean age at first word is greater than 12 months?

(a): Give the associated P-value.

P-value::

(b): Your decision for the hypothesis test:

A. Not enough evidence to know age of first word isn’t 12 months at significance level 4%.
B. Not enough evidence to know age of first word is over 12 months at significance level 4%
C. Age of first word over 12 months at significance level 4%.
D. Age of first word at 12 months at significance level 4%.

4.  An automobile manufacturer would like to know what proportion of its customers are not satisfied with the service provided by the local dealer. The customer relations department will survey a random sample of customers and compute a 95% confidence interval for the proportion who are not satisfied.

(a) Past studies suggest that this proportion will be about 0.18. Find the sample size needed if the margin of the error of the confidence interval is to be about 0.015.
(You will need a critical value accurate to at least 4 decimal places.)
Sample size:

(b) Using the sample size above, when the sample is actually contacted, 15% of the sample say they are not satisfied. What is the margin of the error of the confidence interval?
MoE:

5. Two random samples are taken, one from among first-year UVA students and the other from among fourth-year UVA students. Both samples are asked if they favor modifying the Honor Code. A summary of the sample sizes and number of each group answering yes” are given below:

First-Years (Pop. 1):Fourth-Years (Pop. 2):n1=97,n2=83,×1=63×2=47

Is there evidence, at an α=0.055 level of significance, to conclude that there is a difference in proportions between first-years and fourth-years? Carry out an appropriate hypothesis test, filling in the information requested.

A. The value of the standardized test statistic:

B. The p-value is

C. Your decision for the hypothesis test:

A. Reject H0.
B. Do Not Reject H1.
C. Reject H1.
D. Do Not Reject H0.