A Study Was Conducted to Determine If Husbands and Wives

question 115

Essay

A study was conducted to determine if husbands and wives like the same TV shows. Married couples ranked 15 TV shows, and the Spearman rank correlation coefficient was found to be r_s = 0.47.
A) Specify the competing hypotheses to determine if there is a positive correlation between the two rankings.
B) Assuming the Spearman rank correlation coefficient follows a normal distribution, what are the mean and standard deviation of the normal distribution?
C) Assuming the Spearman rank correlation coefficient follows a normal distribution, what is the value of the test statistic?
D) At the 5% significance level, what is the decision and conclusion?

• A) Specify the competing hypotheses to determine if there is a positive correlation between the two rankings.
• B) Assuming the Spearman rank correlation coefficient follows a normal distribution, what are the mean and standard deviation of the normal distribution?
• C) Assuming the Spearman rank correlation coefficient follows a normal distribution, what is the value of the test statistic?
• D) At the 5% significance level, what is the decision and conclusion?

---

Definitions:

Sample Size

The number of individual observations or data points used in a statistical analysis.

Degrees of Freedom

The total of unique values or figures that may be allocated to a statistical distribution.

Confidence Interval

A range of values, derived from statistical analysis, that is believed to contain the true value of an unknown population parameter with a specified level of certainty.

Degrees of Freedom

The number of independent values or quantities that can vary in the calculation of a statistic, often affecting its distribution.