Question

A psychologist conducted a survey of the attitude towards the sustainability of American energy consumption with 250 randomly selected individuals several years ago. The psychologist believes that these attitudes have changed over time. To test this he randomly selects 250 individuals and asks them the same questions. Can the psychologist confirm his theory that the attitudes have changed from the first survey to the second survey?

Attitude 1st Survey 2nd Survey
Optimistic 7% 6%
Slightly Optimistic 9% 6%
Slightly Pessimistic 31% 37%
Pessimistic 53% 51%
Step 4 of 10: Find the expected value for the number of respondents who are optimistic. Round your answer to two decimal places.

Answer 1

Yes. the Psychologist can confirm his theory that the attitudes have changed over time, based on the first and second surveys.

The expected value for the number of respondents who are optimistic is:

= 16.25

Explanation:

Attitude 1st Survey 2nd Survey

Optimistic 7% 6%

Slightly Optimistic 9% 6%

Slightly Pessimistic 31% 37%

Pessimistic 53% 51%

Expected value of optimistic respondents:

Attitude

Optimistic Expected Value

1st Survey 8.75 (250 * 7% * 50%)

2nd Survey 7.50 (250 * 6% * 50%)

Total EV 16.25