1.We want to estimate pp, 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

Treatment n Cervical cancer cases n Genital wart cases

Gardasil 8487 0 7897 1

Placebo 8460 32 7899 91

(a): Give a 99% 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 99% 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.

15 26 10 9 15 20 18 11 8 20

7 9 10 11 11 10 12 17 11 10

If you treat this as an SRS, does it provide evidence at significance level 5% that the mean age at first word is greater than 12 months?

Give the associated P-value.

P-value::

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

15 26 10 9 15 20 18 11 8 20

7 9 10 11 11 10 12 17 11 10

Treat this as an SRS. Use it to provide a 99% confidence interval of the mean age in months at which children say their first words.

Lower confidence level:

Upper confidence level:

5. Fabrics respond differently to the same dye. Clothing manufacturers need to be able to match the colors of different fabrics. A researcher dyed samples of cotton and of ramie with a dye called procion blue, applied in the same way to each sample. Then she measured the lightness of the color with a colorimeter on a scale in which black is 0, white is 100. Here are the data for 8 pieces of each fabric.

Cotton: 48.82 48.88 48.98 49.04 48.68 49.34 48.75 49.12

Ramie: 41.72 41.83 42.05 41.44 41.27 42.27 41.12 41.49

Do these samples provide evidence significant at the 1% level that the dye affects the cotton and ramie fabrics differently?

Formulate H0H0 and HaHa.

a. Give the test statistic:

b. Give the PP-value: