Task 1

Using Normal Distribution to Analyze Data

Martin suspects that people carry less cash with them than they used to because of credit cards and other cashless payment systems. He decides to work on inventing a new system for people to use in place of cash that would be more user friendly and safe.

Martin conducted a survey to help convince investors to back the development of his new cashless system. One afternoon at the local mall, Martin surveyed a random sample of 95 people and asked the question, How much cash are you carrying in your wallet? The mean of his data is $8.00 with a standard deviation of $2.50. Assume the data is normally distributed. Based on this information, answer the following questions.

Part C

Now, Martin can reasonably guess that the standard deviation for the entire population of people at the mall during the time of the survey is $1.50. What is the 95% confidence interval about the sample mean? Interpret what this means in the context of the situation where 95 people were surveyed and the sample mean is $8. Use the information in this resource to help construct the confidence interval.

Part D

Would the interval found in part C increase, decrease, or remain the same if the confidence level desired were 99%? State your reasoning.

Part E

Would the interval found in part C increase, decrease, or remain the same if fewer than 95 people were surveyed? Justify your answer.

Examining and Interpreting a Statistical Report

To help make his case to potential investors in his invention, Martin found a poll conducted by Gallup, a well-known research organization. Take some time to read the report, and then answer the questions to analyze the merits and limitations of this survey.

Part A

The poll report includes a table titled, "Americans Using Cash Now Versus Five Years Ago, by Age." The age intervals are not equal. Why do you think the Gallup organization chose the age intervals of 23-34, 35-54, and 55+ to display these results?

Part B

In the section describing the survey methods, the report states, "For results based on the total sample of national adults, the margin of sampling error is 4 percentage points at the 95% confidence level." Interpret the meaning of this statement in terms of the poll. Use any statistic given in the report as an example to explain your interpretation.

Part C

In the section describing the survey methods, the report states, "Each sample of national adults includes a minimum quota of 60% cell phone respondents and 40% landline respondents." Do you think this is a good minimum quota for this survey? Should it be lower or higher?

Part D

The report begins by showing three bullet-ed highlights from the survey. At the end of the article, you can click a link to view the complete question responses and trends. Click the link and interpret the results of question 5. Use your interpretation of the statistics to write one more bullet point that could be added as a fourth bullet at the beginning of the report.