Math Problem Statement

Suppose a similar study with the same population was conducted to test the effectiveness of a different drug against the placebo using the exact same directional hypotheses: H subscript 0 colon space space p subscript 1 equals p subscript 2 H subscript A colon space space p subscript 1 less than space p subscript 2 Here, p subscript 1 and p subscript 2 are defined in the same way as above: p subscript 1 equals Pr left curly bracket Yes space vertical line space New space Drug right curly bracket space and space p subscript 2 equals Pr left curly bracket Yes space vertical line space Placebo right curly bracket. However, for this data set, p with hat on top subscript 1 equals 0.36 space and italic space p with italic hat on top subscript italic 2 italic equals italic 0 italic. italic 53. Note that this is not the same data set as in the previous questions; this data set involves a different drug. The R results for this different study are given in below: pearsons chi squared test data: blood clots x-squared=5.8508, df=1, p-value=.01557 What is the P-value for this study? Present your answer rounded to 3 places after the decimal. If the P-value is greater than 0.5 in this study, put 0.5 in the answer blank as your solution.

Solution

The P-value given in the R results is 0.015570.01557. Rounding this to three decimal places, we get:

0.0160.016

Since 0.0160.016 is less than 0.5, this is the final answer.

Answer: P-value=0.016\text{P-value} = 0.016

Would you like more details on interpreting the P-value or any other aspect of this analysis?

Here are five related questions that may enhance your understanding:

  1. What does the P-value indicate in the context of this hypothesis test?
  2. How does the chi-squared statistic relate to the P-value?
  3. Why is rounding to three decimal places often preferred in reporting P-values?
  4. How does a P-value threshold, like 0.05, affect the interpretation of results in hypothesis testing?
  5. What are some limitations of using the chi-squared test for proportions in medical studies?

Tip: When interpreting P-values, remember that a small P-value (typically < 0.05) suggests that the observed data is unlikely under the null hypothesis, supporting evidence for the alternative hypothesis.

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Math Problem Analysis

Mathematical Concepts

Hypothesis Testing
Chi-Squared Test
P-Value Calculation

Formulas

Chi-Squared Statistic Formula: χ² = Σ[(Observed - Expected)² / Expected]
P-Value Interpretation: Based on χ² value and degrees of freedom

Theorems

Chi-Squared Distribution Theorem
Null and Alternative Hypotheses

Suitable Grade Level

Undergraduate Level - Statistics

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