Statistical Studies: Statistical Investigations

III.B Student Activity Sheet 7:

Using Technology

Suppose data were collected on 25 bags of Spud Potato Chips. The weight (to the nearest gram) of the chips in each bag is listed below.

25 28 23 26 2325 25 24 24 2723 24 28 27 2426 24 25 27 2625 26 24 25 25

1. Create a dotplot of the potato chip data and describe the distribution.

2. Does this distribution appear to support or contradict the manufacturer’s claim of an average weight of 28.3 grams of chips per bag?

The average weight appears to be quite a bit below the manufacturer’s claim. Every bag in our sample was below 28.3 grams, but we do not have enough evidence at this time to declare the manufacturer’s claim false.

5. Sometimes it makes sense to analyze the proportion of a population that meets some criterion. This is another method for investigating whether the manufacturer is correct in claiming that the average weight of a bag of Spud’s is 28.3 grams. Write a statement or hypotheses involving the proportion of bags of chips that meet a weight criterion.

We expect that 50% of all bags of chips weigh 28.3 grams or more.

More formally:The true proportion of bags that weigh at least 28.3 grams is 0.5.

Even more formally:Ho: p > 0.5, where p is the true proportion of bags that weigh at least 28.3 gramsHa: p < 0.5(Note: This hypothesis actually refers to the median weight, that 50% of the bags will be more than 28.3 grams and 50% will be less than 28.3 grams.)

6. What proportion of the bags in your sample were 28.3 grams or more? Does the answer change your opinion about Question 2? Why or why not?

100% of the bags in the sample weighed less than 28.3 grams. Answers regarding the opinion about Question 2 may vary. If students were previously unconvinced that the manufacturer’s claim is false, this proportion may convince them.

7. Suppose instead that the weight of the chips in each Spud’s bag is the following:

29 34 22 27 2625 28 24 26 3328 29 31 30 2728 31 28 32 2531 28 30 29 27

Mean = 28.32SD = 2.84Number of data values n = 25The five number summary is 22,26.5,28,30.5,34

Answers may vary, but the average weight is comparable to the manufacturer’s claim, and 64% of the bags weigh 28 grams or more. The data values, however, are much more spread out. The range is 12, from a low of 22 grams to a high of 34 grams.

Statistical Studies: Statistical Investigations

III.B Student Activity Sheet 8:

Survey Design

“School uniforms should not be required.”Agree or disagree?

“Standardized dress can promote a productive school environment.”Agree or disagree?

These questions show that the design of a survey can influence the results. Questions should be designed to be neutral and to allow the accurate recording of the opinions or facts given by the participants. For example, the uniform question could be worded as follows:

I am in favor of school uniforms for high school students.Strongly agree Agree No opinion Disagree Strongly disagreeThis is an example of a closed question because the participants are limited to the response choices that are given. Closed questions are easier (and usually cheaper) to analyze, and sometimes a computer does much of the work. Open questions allow the participants to give more detailed responses. This approach, however, requires a follow-up analysis that is more labor intensive (and more expensive).1. Reword the school uniform question so that it is an open question.

Describe your opinions about school uniforms for high school students.

Because the design of a survey is so important for capturing the information needed accurately, pilot surveys are often conducted. A pilot survey is used with a small number of people and then analyzed to look for the following:

• question ambiguity,• leading questions,• too many people choosing Other or No opinion, and• other data collection problems.

2. The following questions can be worded more effectively. Describe the question’s problem and what effect the problem could have on the results. Then come up with more effective wording for the question. Provide a closed question and an open question.

a. I can always talk to my parents about my problems. True/False

People rarely commit to always or never on anything. This word leads them to answer False . The report would indicate that teens do not talk to their parents at all.

Closed question:I talk to my parents about my problems.Always Usually Sometimes Rarely Never

Open question:Describe your relationship with your parents. Do you talk to them about your problems?

b. Teachers and students like the new school schedule. True/False

Lumping teachers and students together muddies the results. Some may agree that teachers like the new schedule but not students, or vice versa. Some in this position may answer True while others answer False when really they feel the same way. Prepare separate questions for teachers and students. Possibly separate survey instruments for the two groups.

Closed question:I like the new schedule.

Agree Somewhat agree Neutral Somewhat disagree Disagree

Open question:Describe your feelings about the new school schedule.

c. I like the school cafeteria. True/False

This question is too broad and produces no useful information. If people select False , we still do not know what they do not like. Therefore, there is no guidance for improvement.

d. I support school activities. True/False

This question is too broad and produces no useful information. Participants may not know which answer to select if they support some activities and not others. In the end, we will not know which activities students like, or if they do not like any of them at all.Closed question: (Check a box for each activity.) Activity I participate

in this activity.

Theater

Choir

Band

Football

[other examples]Other:

Open questions:• Which school activities do you participate in?• Which school activities do you support?• Which activities should not be part of the school day?

I supportthisactivity.

I amneutralabout thisactivity.

I wish thisactivity wascancelled.

When designing a survey (or an observation instrument), the researcher must also considerhow the data will be collected. The following are some options:a. A face-to-face interviewer asks questions and records the answers of the participants(on paper or an electronic recording).b. A telephone interviewer asks questions and records the answers.c. A computer calls homes and records answers through key presses.d. A researcher observes behaviors or characteristics and marks the survey.e. A researcher hand-delivers surveys to participants, who then fill out the surveys and turn them back in.f. The survey is mailed to participants.g. The survey is e-mailed to participants.

3. Discuss the pros and cons of each method with your partner(s). Record your observations.