Statistic

1. (6)

It has been suggested that the average Facebook user spends 6 hours a week on the site. If we

assume a normal distribution, with a population standard deviation of 3 hours…

i.(3)

What percentage of users spend more than 9 hours on Facebook?

ii.(3)

What p

ercentage of users spend between 2 and 4 hours on Facebook?

2. (6)

On final exams, Sarah scored 90 in Economics and Martha scored 85 in Geography. We can assume

that the students’ scores within each subject are approximately “normal” in distribution. The

mean scores

in Economics and Geography were both 72. The standard deviation in Economics was 12 points, while in

Geography it was 8.

Which of the two students has a better score, compared with his/her fellow students? Please show how you

arrived at your

conclusion.

3. (4)

What is the difference between random sampling, stratified random sampling, and cluster sampling? How

might random sampling of the entire population in the US help us understand the current spread of COVID

-

19,

rather than just testing

people who show symptoms?

4. A group of researchers at the University of Texas

-

Houston conducted a comprehensive study of

pregnant cocaine

-

dependent women (

Journal of Drug Issues

, Summer 1997). All the women in the study

used cocaine on a regular basis for

more than a year. One of the many variables measured was birth

weight (in grams) of the baby delivered. For a sample of 16 cocaine

-

dependent women, the mean birth

weight was 2,971 grams and the standard deviation was 410 grams. Test the hypothesis that th

e true

mean birth weight of babies delivered by cocaine

-

dependent women is less than 3,100 grams. Use alpha =

.05.

5. (3)

Confidence bands for population means are smaller if you (1) know the standard deviation of the

population, instead of estimating it

from the sample, or (2) if you decrease the level of confidence

required. In addition to these two possibilities, how else could you obtain a smaller confidence band?

6. (3)

We can calculate confidence bands for means by using z

-

values from a normal dis

tribution table (or t

-

values

from a t

-

distribution table), even if the population under study is not normally distributed. Briefly explain the

property of random samples that makes this possible.

1. (6) It has been suggested that the average Facebook user spends 6 hours a week on the site. If we

assume a normal distribution, with a population standard deviation of 3 hours…

i.(3) What percentage of users spend more than 9 hours on Facebook?

ii.(3) What percentage of users spend between 2 and 4 hours on Facebook?

2. (6) On final exams, Sarah scored 90 in Economics and Martha scored 85 in Geography. We can assume

that the students’ scores within each subject are approximately “normal” in distribution. The mean scores

in Economics and Geography were both 72. The standard deviation in Economics was 12 points, while in

Geography it was 8.

Which of the two students has a better score, compared with his/her fellow students? Please show how you

arrived at your conclusion.

3. (4) What is the difference between random sampling, stratified random sampling, and cluster sampling? How

might random sampling of the entire population in the US help us understand the current spread of COVID-19,

rather than just testing people who show symptoms?

4. A group of researchers at the University of Texas-Houston conducted a comprehensive study of

pregnant cocaine-dependent women (Journal of Drug Issues, Summer 1997). All the women in the study

used cocaine on a regular basis for more than a year. One of the many variables measured was birth

weight (in grams) of the baby delivered. For a sample of 16 cocaine-dependent women, the mean birth

weight was 2,971 grams and the standard deviation was 410 grams. Test the hypothesis that the true

mean birth weight of babies delivered by cocaine-dependent women is less than 3,100 grams. Use alpha =

.05.

5. (3) Confidence bands for population means are smaller if you (1) know the standard deviation of the

population, instead of estimating it from the sample, or (2) if you decrease the level of confidence

required. In addition to these two possibilities, how else could you obtain a smaller confidence band?

6. (3) We can calculate confidence bands for means by using z-values from a normal distribution table (or t-values

from a t-distribution table), even if the population under study is not normally distributed. Briefly explain the

property of random samples that makes this possible.