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:
To find the chi-square value for a one-tailed hypothesis test at a 95% confidence level with a sample size of 25, we need to consider the following:
- Degrees of Freedom: In a chi-square test, the degrees of freedom (df) are calculated as: df=n−1df = n – 1 where nn is the sample size. In this case, with a sample size of 25, the degrees of freedom would be: df=25−1=24df = 25 – 1 = 24
- Chi-Square Table Lookup: For a one-tailed upper test at a 95% confidence level, we are looking for the critical value corresponding to a 0.05 significance level (since 1 – 0.95 = 0.05) with 24 degrees of freedom.
- Using a Chi-Square Distribution Table: By referencing a chi-square distribution table for 24 degrees of freedom and a 0.05 significance level (upper tail), the corresponding chi-square value is approximately 37.6525.
This value is critical for determining the threshold beyond which the observed test statistic would be considered statistically significant at the 95% confidence level. If the calculated chi-square statistic exceeds this critical value, the null hypothesis would be rejected, indicating that the observed data significantly deviates from the expected distribution.
In summary, the chi-square value for a one-tailed (upper tail) hypothesis test at 95% confidence and a sample size of 25 is 37.6525.