What Conclusion Would Be Appropriate for an Upper-Tailed Chi-Squared Test $\alpha = .05 , \text { df } = 4 , { \chi } ^ { 2 } = 14.69$

question 10

Essay

What conclusion would be appropriate for an upper-tailed chi-squared test in each of the following situations?
a. $\alpha = .05 , \text { df } = 4 , { \chi } ^ { 2 } = 14.69$
b. $\alpha = .01 , d f = 3 , \chi ^ { 2 } = 7.85$
c. $\alpha = .10 , d f = 2 , { \chi } ^ { 2 } = 4.42$
d. $\alpha = 01 , k = 6 , \chi ^ { 2 } = 13.92$

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Definitions:

Sampling Distribution

The statistical distribution that represents the probability of various outcomes, originating from a vast number of samples from a targeted population.

Standard Deviation

The square root of the variance showing how much individual data points differ from the mean.

Central Limit Theorem

A statistical principle stating that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the population's distribution.

Sampling Distribution

The likelihood distribution of a statistic derived from numerous samples taken from a particular population.