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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?

Definitions:

Security's Beta

A measure of a stock's volatility in comparison to the overall market; a beta greater than 1 indicates higher volatility than the market, while a beta less than 1 indicates lower volatility.

Security Market Line

A line that represents the relationship between risk and expected return in capital market theory, often used in the capital asset pricing model.

Beta

Beta is a measure of a stock's volatility in relation to the overall market; a beta greater than 1 indicates that the stock is more volatile than the market, while a beta less than 1 means it is less volatile.

Regression Line

A straight line that best fits the data points in a scatter plot, used in statistics to model the relationship between two variables.