Question

Assignment 4

As part of a series of tests of the abilities of professional astrologers, the following study was conducted. Professional astrologers prepared horoscopes (a description of the characteristics of the individual based on the alignment of stars when they were born) of 83 different randomly selected adults from San Diego, California. Each individual in the study was then shown three different horoscopes—the one prepared for them, along with two others. Each individual then needed to select the correct horoscope. Twenty-eight out of 83 adults selected the correct horoscope.

1. Identify the population of interest.
   
   
2. Identify the sample.
   
   
3. Describe, in words, the relevant parameter of interest.
   
   
   
4. State the null and alternative hypothesis testing if adults can choose their correct horoscope more often than if they were just guessing.
   
   
   

5. The p-value obtained from this test using a theory-based approach is 0.4715. State an appropriate conclusion.

6. In your own words explain how a randomized experiment controls confounding variables, and why a cause-effect conclusion is possible in a randomized experiment.

Answer 1

(a) The population of interest is all the adults from San Diego, California.

(b) The sample is Twenty-eight adults from San Diego, California.

(c) The relevant parameter of interest is adults who selected the correct horoscope.

(d) The hypothesis being tested is:

H₀: Adults cannot choose their correct horoscope more often than if they were just guessing

H_a: Adults can choose their correct horoscope more often than if they were just guessing

(e) Since the p-value (0.4715) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that adults can choose their correct horoscope more often than if they were just guessing.