The chi-square value for a one-tailed (upper tail) hypothesis test at 95% confidence and a sample size of 25 is
Select one:
a. 39.3641
b. 37.6525
c. 36.4151
d. 33.1963
The correct answer and explanation is:
The correct answer is b. 37.6525.
Explanation:
The chi-square test is commonly used to test hypotheses about variances or to assess goodness of fit. The chi-square distribution is widely used in statistical hypothesis testing, especially in the context of variances and categorical data.
For a one-tailed (upper tail) hypothesis test, you are interested in determining the critical value where the upper tail area corresponds to the desired confidence level. In this case, the hypothesis test is conducted at a 95% confidence level, meaning the alpha level (α\alpha) is 0.05, and you are looking for the critical value that corresponds to the upper 5% of the chi-square distribution.
How to find the chi-square critical value:
The chi-square distribution depends on the degrees of freedom (df), which is determined by the sample size. For this case, the sample size is 25, so the degrees of freedom are calculated as: df=n−1=25−1=24df = n – 1 = 25 – 1 = 24
Next, the chi-square critical value for a one-tailed test is located by looking up the value corresponding to the upper 5% (i.e., 0.05) in a chi-square distribution table, using 24 degrees of freedom. From standard chi-square distribution tables or using statistical software, the chi-square critical value for df = 24 at α=0.05\alpha = 0.05 is approximately 37.6525.
This value indicates the threshold beyond which you would reject the null hypothesis if your calculated chi-square statistic exceeds this value. Thus, if the chi-square value from your data is greater than 37.6525, you would conclude that the observed data is inconsistent with the null hypothesis at the 95% confidence level.
To summarize:
- Sample size: 25
- Degrees of freedom (df): 24
- Confidence level: 95%
- Critical chi-square value: 37.6525