13C

State Average Daily Screen Time

(in minutes)

   State Average Daily Screen Time (in minutes)
Alabama 170 Montana 154
Alaska 134 Nebraska 182
Arizona 276 Nevada 262
Arkansas 145 New Hampshire 135
California 204 New Jersey 182
Colorado 166 New Mexico 177
Connecticut 262 New York 206
Delaware 166 North Carolina 205
Florida 213 North Dakota 192
Georgia 198 Ohio 231
Hawaii 133 Oklahoma 131
Idaho 161 Oregon 132
Illinois 220 Pennsylvania 213
Indiana 220 Rhode Island 165
Iowa 163 South Carolina 155
Kansas 146 South Dakota 154
Kentucky 149 Tennessee 196
Louisiana 144 Texas 186
Maine 165 Utah 155
Maryland 199 Vermont 124
Massachusetts 195 Virginia 179
Michigan 188 Washington 173
Minnesota 140 West Virginia 150
Mississippi 146 Wisconsin 211
Missouri 211 Wyoming 134
Symbol Description
difference between the population means
population mean of Group 1
sample standard deviation of Group 1
sample size of Group 1
sample mean of Group 2
difference between the sample means
sample mean of Group 1
population mean of Group 2
sample size of Group 2
sample standard deviation of Group 2
Group 1:

smoke_now = Yes

Mothers who smoked during pregnancy

 Group 2:

smoke_now = No

Mothers who did not smoke during pregnancy
Sample Mean 114  = 123
Sample Standard Deviation = 18.2 = 17.3
Sample Size = 480 = 733
Group 1: Female Professors Group 2: Male Professors
Sample Size 40 53
Sample Mean Course Evaluation Score 3.79 4.01
Sample Standard Deviation 0.51 0.53
Community College Transfer (Group 1) No Transfer (Group 2)
Sample Size 267 1176
Sample Mean Time to Graduate, in Years 5.37 4.45
Sample Standard Deviation Time to Graduate, in Years 1.175 1.001
gestation smoke smoke_now age wt
284 never No 27 120
282 never No 33 113
279 now Yes 28 128
282 now Yes 23 108
286 until current pregnancy No 25 136
244 never No 33 138
245 never No 23 132
289 never No 25 120
299 now Yes 30 143
351 once did, not now No 27 140
Group 1:

smoke_now = Yes

Mothers who smoked during pregnancy

 Group 2:

smoke_now = No

Mothers who did not smoke during pregnancy
Sample Mean  

= ____
Sample Standard Deviation  

= ______

 

  

= ______

 
 

Sample Size

  

= ______

 

  

= _____

 
Skill or Concept: I can . . . Questions to check your understanding Rating
from 1 to 5
Use appropriate notation to represent the sample mean, sample standard deviation, and sample size for multiple groups. 1, 2
Write an expression that represents the difference between two sample means and the difference between two population means. 3
Verify that conditions are met for a two-sample t-test for independent samples. 4
Calculate the standard error for a sampling distribution and interpret its meaning. 5
Use descriptive statistics to describe the difference between two sample means and interpret its meaning. 6, 7

text reading "Bias in selection. Selection of mothers by smoking habit may result in a study population consisting of two groups that are dissimilar in other respects. The basic problem is that some well-known risk factors affecting mortality are also independently related to the frequency of smoking." The output from a data analysis tool. In the top left, there is a heading reading “Descriptive Statistics.” Beneath it is a table with columns “Group,” “Sample Size,” “Mean,” and “Standard Deviation.” The first row reads “Male Politicians” under Group, 30 under Sample Size, 10.7 under Mean, 26.3 under standard deviation. The second row reads “Female Politicians” under Group, 30 under Sample Size, -1.1 under Mean, and 27.9 under standard deviation. Beneath this table is another table, titled “Test Statistic.” It has columns “Observed Difference,” “Standard Error,” “Test Statistic t,” and “dt.” Their values are 11.8, 7.0, 1.681, and 57.8, respectively. There is another table beneath this labeled “Hypothesis Test.” It has the columns “Population Parameter,” “Null Hypothesis,” “Alternative Hypothesis,” “Test Statistic t,” and “P-value.” Under population parameter, it reads “Difference mu sub one - mu sub two,” under null hypothesis, it reads “mu sub one - mu sub two = 0,” under alternative hypothesis, it reads “mu sub one - mu sub two does not equal 0,” under test statistic t, it reads 1.681, and under p-value, it reads 0.0981. To the right of these tables is a box plot labeled “Dominance” on the y-axis. For “Male Politicians,” the low end is at approximately -40 and the high end is at approximately 50. The low point of the box is at approximately 10 and the high end is at approximately 30. The middle line is at approximately 20. For “Female Politicians,” the low end is at approximately -40 and the high end is at approximately 70. The low point of the box is at approximately -25 and the high point is at approximately 20. The middle line is at approximately 0. Beneath this box plot and the tables, there is a graph titled “t Distribution with dt = 57.8” with a subheading reading “H sub 0: mu sub 1 equals mu sub 2, H sub a: mu sub 1 does not equal mu sub 2. Test Statistic: t = 1.681, P-value = 0.0981.” The graph below shows a curve with a peak centered on approximately 0. There are dotted vertical lines at -1.68 and 1.68. The area outside these lines under the curve is shaded and on each side is labeled 0.0491. The area between the lines under the curve is a lighter shade and is labeled 0.9019.

Glossary

two-sample t-test
a hypothesis test for comparing two population means.