Graduates of a two year associate degree nursing program (AND) and graduates of a four year baccalaureate nursing program (BSN) both take the same certificate exam for licensure as a registered nurse. It has been argued that the two year program is too short, and that undergraduate nursing education should be standardized to a four year program. The state board exam scores for AND and BSN graduate’s are considered. Of 80 AND graduates, 60 passed. Of 115 BSN graduates, 95 passed. Do the two groups perform differently? (a=.05) Using confidence interval can some break it down into steps
To determine if the two groups (AND and BSN graduates) perform differently, we can perform a hypothesis test using the given information.
Step 1: State the hypothesis
The null hypothesis (H0): There is no difference in performance between AND and BSN graduates.
The alternative hypothesis (Ha): There is a difference in performance between AND and BSN graduates.
Step 2: Calculate the test statistic
We can use the chi-square test statistic to compare the observed frequencies to the expected frequencies (assuming no difference). The formula for the chi-square test statistic is:
χ² = Σ((O - E)² / E)
Where:
O = Observed frequency
E = Expected frequency
Σ = Summation (the sum of the calculated values for all groups)
In this case, we have two groups: AND graduates and BSN graduates.
Let's calculate the expected frequencies first:
The total number of graduates is 80 + 115 = 195.
The proportion of AND graduates is 80/195 = 0.41.
The proportion of BSN graduates is 115/195 = 0.59.
Expected frequencies for AND graduates:
Expected pass: 0.41 * 60 = 24.6
Expected fail: 0.41 * (80 - 60) = 8.2
Expected frequencies for BSN graduates:
Expected pass: 0.59 * 95 = 56.05
Expected fail: 0.59 * (115 - 95) = 11.8
Now, we can calculate the chi-square test statistic:
χ² = ((60 - 24.6)² / 24.6) + ((20 - 8.2)² / 8.2) + ((95 - 56.05)² / 56.05) + ((20 - 11.8)² / 11.8)
Step 3: Determine the critical value
With a significance level (a) of 0.05, we would compare the calculated chi-square statistic to the critical chi-square value with appropriate degrees of freedom. The degrees of freedom in this case are (R - 1) * (C - 1), where R is the number of rows (2) and C is the number of columns (2).
Using a chi-square distribution table or software, we can find the critical chi-square value at the desired level of significance (df = 1, α = 0.05).
Step 4: Make a decision
If the calculated chi-square statistic is greater than the critical chi-square value, we reject the null hypothesis and conclude that there is a difference in performance between AND and BSN graduates. Otherwise, we fail to reject the null hypothesis.
Step 5: Calculate the p-value (optional)
If you want to calculate the p-value to provide more evidence, you can find the p-value associated with the calculated chi-square statistic using the chi-square distribution table or software. If the p-value is less than the significance level (a), we reject the null hypothesis.
By following these steps, you can determine if the two groups (AND and BSN graduates) perform differently based on the given data.