A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 308 people over the age of 55, 61 dream in black and white, and among 306 people under the age of 25, 15 dream in black and white. Use a 0.01 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25. Complete parts (a) through (c) below. a. Test the claim using a hypothesis test. Consider the first sample to be the sample of people over the age of 55 and the second sample to be the sample of people under the age of 25. What are the null and alternative hypotheses for the hypothesis test? OC. Ho: P₁ P₂ OA Ho: P₁ P2 OB. Ho: P₁ P2 H₁: P₁ P2 H₁: P₁ P₂ H₁: P₁ P₂ F. Ho: P1 P2 OD. Ho: P₁ P2 OE. Ho: P₁ SP₂ H₁: P₁ P₂ H₁: P₁ P₂ H₁: P₁ P2 Identify the test statistic. z = 5.61 (Round to two decimal places as needed.) Identify the P-value. P-value=0 (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? reject the null hypothesis. There is sufficient evidence to support the claim that the proportion of people over 55 who dream in black and white is greater than the The P-value is less than the significance level of a = 0.01, so proportion for those under 25. b. Test the claim by constructing an appropriate confidence interval. The 98% confidence interval is < (P₁-P₂) <0 (Round to three decimal places as needed.)