Statistics

Statistics

Chapter 7-T tests with Two Samples
1-2 One of the following tests is a two related sample/matched pairs T test and the other is a two independent sample T test. The first thing that you should decide is what type of test you are dealing with. (Refer to Lab 10 for test details in StatCrunch.)

1. How do superstitions associated with Friday the 13th affect human behavior? Friday the 13th is seen as a very unlucky date to many. A group of researchers in the UK collected data on traffic and shopping patterns and accident frequency for Fridays the 6th and 13th between October of 1989 and November of 1992. The only data that revealed a Normal distribution was the traffic pattern data, so this is what we will look at. (The other variables were not Normal and lacked the large sample size needed to use the t-test without assumption of Normality.)

The data (on Blackboard) was obtained by the researchers from the British Department of Transport regarding the traffic flows between junctions 7 to 8 and junctions 9 to 10 of the M25 motorway.

(Source: Scanlon, T.J., Luben, R.N., Scanlon, F.L., Singleton, N. (1993), "Is Friday the 13th Bad For Your Health?," BMJ, 307, 1584-1586.)

a) First find the differences between the number of cars passing through these two intersections on the specified dates on Friday the 13th and Friday the 6th. (This may be done in StatCrunch as part of your test.)
b) What type of T test should you use? How did you decide this?
c) Based on this data, do significantly fewer drivers travel on roads in the UK on Friday the 13th? Use the significance level =.05.

2. An experiment was done to test whether directed reading activities in the classroom help elementary school students improve aspects of their reading ability. A treatment class of 21 third-grade students participated in these activities for eight weeks, and a control class of 23 third-graders followed the same curriculum without the activities. After the eight-week period, students in both classes took a Degree of Reading Power (DRP) test which measures the aspects of reading ability that the treatment is designed to improve. The results can be seen in the data file on Blackboard.
(Source: Schmitt, Maribeth C., The Effects on an Elaborated Directed Reading Activity on the Metacomprehension Skills of Third Graders, Purdue University, 1987.)

a) Does this research provide significant evidence, at the 5% level, that the directed reading activities improve some aspects of elementary school students reading abilities? State hypotheses and use the appropriate T test.
b) Is there significant evidence at the 2.5% level?
c) What other information (i.e., possible lurking variables) would you want to know here to be convinced directed reading is an effective method?



Chapter 8-Significant Tests Based on Proportions
Recall that on StatCrunch the Z tests for proportions are listed under Proportions and not under Z statistics. For complete instructions please refer back to Lab 10.



3. In November/December 2009 there was much debate over the recently released opinion of a task force that advised that women get their first mammogram at age 50 (as opposed to the previously recommended age 40) and then continue to get a mammogram every other year (as opposed to every year). Gallup presented the following data based on their poll conducted November 20-22, 2009 with a total sample size of 1,136 women aged 35-75.

a) I want you to use the information from the poll to calculate a 98% confidence interval for the proportion of women (aged 35-75) who disagree (combining both Strongly Disagree and Disagree) with the new recommendation.


b) What is the margin of error for your confidence interval found in a)? Explain what this margin of error is telling you. Specifically, what types of error does this account for and what types does it not account for?

c) Is there significant evidence at level 5% that most women (i.e. more than 50%) in the designated age group do not agree with the new recommendation? State your hypotheses, test statistic, P-value, and conclusion.












Chapter 9-Chi-Square

Recall from class: For a Chi-Square Test with two variables you may have the original categorical data entered into two columns. Once the data is loaded you can select STATTablesContingencyWith Data.
Alternatively, you may enter the observed frequencies into StatCrunch as a contingency table. Recall that this means that the row labels are in the first column. Column labels can go in var2, var3, etc. Enter the appropriate frequencies and then select STATTablesContingencyWith Summary.
Either way, once you select the appropriate columns and hit Calculate you will see the contingency table, test stat and p-value. There are additional options to display the conditional distributions (row percents and column percents) and the expected frequencies (counts). We used these back in Chapter 2.


4. For the purposes of government statistics an American is in the work force if they are available for work and either working or actively seeking work. They use this information to find unemployment rates. The data below is from a survey in a recent year (obviously not this year) for the civilian labor force of those ages 25 years and older. Each table entry is a count in thousands of people.

Highest Education Employed Unemployed
Did not Finish High School 11139 934
High School but No College 35137 1718
Less than Bachelors 31975 1356
College Graduate 36259 1022


a) I believe that there is a relationship between education and unemployment. Does the data support this claim? State an appropriate null hypothesis and use significance testing to answer this question.


b) Find any conditional distributions that support your answer from part a and add to your conclusions.