Math  /  Data & Statistics

QuestionA new vaccination is being used in a laboratory experiment to investigate whether it is effective. There are 227 subjects in the study. Is there sufficient evidence to determine if vaccination and disease status are related? \begin{tabular}{|c|c|c|c|} \hline Vaccination Status & Diseased & Not Diseased & Total \\ \hline Vaccinated & 41 & 103 & 144 \\ \hline Not Vaccinated & 59 & 24 & 83 \\ \hline Total & 100 & 127 & 227 \\ \hline \end{tabular} Copy Data
Step 1 of 8: State the null and alternative hypothesis.
Answer Tables Keypad Keyboard Shortcuts H0H_{0} : vaccination and disease status are independent HaH_{a} : vaccination and disease status are dependent H0H_{0} : vaccination and disease status are dependent Ha:H_{a}: vaccination and disease status are independent Submit Answer

Studdy Solution

STEP 1

1. We are conducting a hypothesis test to determine if there is a relationship between vaccination status and disease status.
2. We will use a chi-square test for independence.

STEP 2

1. State the null and alternative hypotheses.
2. Set up the contingency table.
3. Calculate the expected frequencies.
4. Compute the chi-square statistic.
5. Determine the degrees of freedom.
6. Find the critical value or p-value.
7. Make a decision to accept or reject the null hypothesis.
8. Interpret the results.

STEP 3

State the null and alternative hypotheses:
- Null Hypothesis (H0H_0): Vaccination and disease status are independent. - Alternative Hypothesis (HaH_a): Vaccination and disease status are dependent.

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