DS-203 - Western Illinois University



Homework 1

Due: Monday February 8

DS-503

Fall 2009

Show All your Work

Round your final answer to two decimal places

1. The Survey of Study Habits and Attitudes (SSHA) is a test that evaluates college student’s motivation, study habits, and attitude toward school. The SSHA data for 19 first year college women are:

154, 109, 137, 115, 152, 140, 154, 178, 101,

103, 126, 126, 137, 165, 165, 129, 200, 148, 138

The SSHA scores for 20 first-year college men are:

108, 140, 114, 91, 180, 115, 126, 92, 169, 146,

109, 132, 75, 88, 113, 151, 70, 115, 187, 104

For the above two data sets

1) Make a back-to-back stem and leaf graph.

2) Find the five-number summaries.

3) Make a side –by-side box plots of the distribution

4) Find the mean and standard deviation for the two groups.

You can use the following information:

Table for the SSHA scores for 20 first-year college men are:

|  |X |X2 |Ordered X |

|1  |108 |11664 |70 |

| 2 |140 |19600 |75 |

| 3 |114 |12996 |88 |

| 4 |91 |8281 |91 |

| 5 |180 |32400 |92 |

| 6 |115 |13225 |104 |

| 7 |126 |15876 |108 |

| 8 |92 |8464 |109 |

| 9 |169 |28561 |113 |

| 10 |146 |21316 |114 |

| 11 |109 |11881 |115 |

| 12 |132 |17424 |115 |

| 13 |75 |5625 |126 |

| 14 |88 |7744 |132 |

| 15 |113 |12769 |140 |

| 16 |151 |22801 |146 |

| 17 |70 |4900 |151 |

| 18 |115 |13225 |169 |

| 19 |187 |34969 |180 |

| 20 |104 |10816 |187 |

|Total |2425 |314537 |  |

Table for the SSHA scores for 19 first-year college women are:

|n  |Y |Y2 |ordered Y |

|1  |154 |23716 |101 |

| 2 |109 |11881 |103 |

| 3 |137 |18769 |109 |

| 4 |115 |13225 |115 |

| 5 |152 |23104 |126 |

| 6 |140 |19600 |126 |

| 7 |154 |23716 |129 |

| 8 |178 |31684 |137 |

| 9 |101 |10201 |137 |

| 10 |103 |10609 |138 |

| 11 |126 |15876 |140 |

| 12 |126 |15876 |148 |

| 13 |137 |18769 |152 |

| 14 |165 |27225 |154 |

| 15 |165 |27225 |154 |

| 16 |129 |16641 |165 |

| 17 |200 |40000 |165 |

| 18 |148 |21904 |178 |

| 19 |138 |19044 |200 |

|Total |2677 |389065 | |

2. Product designers often must consider physical characteristics of their target population. For example, the distribution of heights of men aged 20 to 29 years is approximately normal with mean 69 inches and standard deviation 2.5 inches. Use the 68-95-99.7 rule to answer the following questions.

a) What percent of these men are taller than 74 inches?

b) Between what heights do the middle 95% of young men fall?

c) What percent of young men are shorter than 66.5 inches?

d) What percent of young men are between 71.5 and 74 inches?

3. The Environmental Protection Agency requires that the exhaust of each model of motor vehicle be tested for the level of several pollutants. The level of oxides of nitrogen (NOX) in the exhaust of one light truck model was found to vary among individual trucks according to a normal distribution with mean 1.5 grams per mile driven and standard deviation 0.40 grams per mile.

a) What percent of trucks of this model have more than 1.15 grams of NOX in their exhaust?

b) What percent of trucks of this model have between 1.35 and 1.55 grams of NOX in their exhaust?

c) How much is the NOX level of the upper 10% of this model truck?

4. A sample was taken of the salaries of 20 employees of a large company. The following are the salaries (in thousands of dollars) for this year. For convenience, the data are ordered.

|28 |31 |

|A) |is 1. |

|B) |is 2. |

|C) |is 3. |

|D) |cannot be determined from the information given. |

|2. |The mean age of five people in a room is 30 years. One of the people whose age is 50 years leaves the room. The mean age of |

| |the remaining four people in the room is |

|A) |40. |

|B) |30. |

|C) |25. |

|D) |not able to be determined from the information given. |

|3. |The median age of five people in a meeting is 30 years. One of the people, whose age is 50 years, leaves the room. The median |

| |age of the remaining four people in the room is |

|A) |40 years. |

|B) |30 years. |

|C) |25 years. |

|D) |not able to be determined from the information given. |

|4. |A set of data has a median that is much larger than the mean. Which of the following statements is most consistent with this |

| |information? |

|A) |A stemplot of the data is symmetric. |

|B) |A stemplot of the data is skewed left. |

|C) |A stemplot of the data is skewed right. |

|D) |The data set must be so large that it would be better to draw a histogram than a stemplot. |

|5. |When creating a scatterplot, one should |

|A) |use the horizontal axis for the response variable. |

|B) |use the horizontal axis for the explanatory variable. |

|C) |use a different plotting symbol if the explanatory variable is categorical than if the response variable is categorical. |

|D) |use a plotting scale that makes the overall trend roughly linear. |

|6. |A study is conducted to determine if one can predict the price of a stock based on the price to earnings ratio. The response |

| |variable in this study is |

|A) |price of the stock. |

|B) |the price to earnings ratio. |

|C) |the researcher. |

|D) |either the NASDAQ or the Dow Jones Industrial Average. |

7. In order to rate TV shows, phone surveys are sometimes used. Such a survey might record several variables, some of which are listed below. Which of these variables are categorical?

A) The number of persons watching the show.

B) The ages of all persons watching the show.

C) The number of times the show has been watched in the last month.

D) The name of the show9if any being watched.

8. Which of the following is not true regarding the advantages of the mean as a measure of location?

A) The mean is relatively insensitive to skewness in data?

B) The mean uses all the values in the data set.

C) The mean is uniquely defined for a given set of data.

D) All of the above are true.

9. You are told that your score on an examination was at the 60th percentile. Your score was

A) above the third quartile

B) between the median and the third quartile

C) between the first quartile and the median

D) below the first quartile

E) non of the above.

10. When the mean and median are approximately equal the distribution of values in the sample is

A) Negatively skewed.

B) Positively skewed.

C) Approximately symmetric

D) Cannot answer, there is not enough information

E) None of the above

Use the following problem for questions 11 -15.

A resort hotel is interested in how far people travel to reach the hotel. Eight guests are interviewed, and each is asked the distance (in miles) from their home to the hotel. The resulting data is given below.

80 850 120 200 210 50 25 190

11. The sample mean is;

a. 155

b. 215.6

c. 265.8

d. None of the above

12. The sample standard deviation is

a. 155

b. 215.6

c. 265.8

d. None of the above

13. The sample variance is

a. 70667.4

b. 61833.98

c. 2704

d. None of the above

14. Suppose the investigator finds out that the number 85 was recorded wrongly as 850. If we use the correct number (85) in our computations which of the following statistics will be affected more?

a. Mean

b. Median

c. Mode

d. None of the above

15. Scores on a standardized exam have a mean of 120 and standard deviation of 15. What z-score corresponds to test score of 150?

a. -2

b. 2

c. -1

d. 3

e. None of the above

16. The area under the standard normal for Z< -2.25 is:

a. .975

b. .0125

c. .0122

d. .0119

e. None of the above

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