Homework 2

25 points

Directions: Please write neatly and place a square around your final answer. Use a separate sheet of paper to provide your answers and show your work. You do not have to re-write the question.

1.Rebecca's son has taken a speech competency test and has a z-score of -1.2 (the son scored 1.2 standard deviations below the mean)

Mean Test Score= 120

Standard Deviation= 12

a.If their z-score was z = -1.2, what was Rebecca's son's test score? (2 points)

b.On his second attempt, Rebecca's son scores a 110. Calculate the son's z-score and interpret your answer (2 points)

2.Consider the following data and answer the provided questions

The average age at which 1^st child is born = 30.3 years old

Standard Deviation = 2.8

a. If someone has their first child at 25 years old, how many standard deviations from the mean are they? In other words find their z-score by converting their age (y = 25) into a Z. (2 points)

b. How old is someone who has a z-score of +2.35z? In other words, convert z = 2.35 into a y-score. (2 points)

3.If the mean number of children in a normally distributed sample is 2 children and a respondent's z = 0, how many children do they have? (2 points)

4.Create a systematic sample of n=5 using the K method for the following 15 names. Simply state the names that would end up in your sample. (4 points)

Jesse, James, Patty, Allie, Sophia, Holden, Fabio, Desmond, Terrance, Glenn, Travis, Donna, Stan, Damien, Karl

5.State whether you would use proportionate stratified sampling or disproportionate stratified sampling in the following scenarios. Explain your reasoning.

a.Sheryl is conducting a study comparing the health of Asian women over 60 in Orange County with the rest of population. However, only 1% of Orange County is made up of Asian Women over 60. (2 points)

b.Researchers at the Social Science Research Center want to ensure their study on religious life among L.A. resident truly represents the actual racial demographic in L.A. L.A. is made up of 47.5% Hispanic or Latino residents of any race, 29.4% non-Hispanic whites, 10.7% Asian, 9.8% Black or African American, and 2.6% other or mixed race.

(2 points)

6.A sample of 70 students report an average of 5 hours of studying per week with a standard deviation of 4.5. Calculate the confidence interval of the mean at the 95% confidence level.

(3 points)

7.Among a sample 60 expectant mothers, 59% reported receiving financial help from friends or family in the past year. Calculate the confidence interval of proportions at the 99% confidence level. (4 points)