We are interested in whether the proportions of female suicide victims for ages 15 to 24 are the same between the white and the black races in the United States. We randomly pick one year to compare the races. The number of suicides estimated in the United States in that year for white females is 4,930. Five hundred eighty-three were aged 15 to 24. The estimate for black females is 330. Forty-one were aged 15 to 24. We will let female suicide victims be our population. (Use α = 0.05.) NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part (a) State the null hypothesis. ○ Ho: PW> PB O Ho: PW + PB Ho: Pw≤ PB Ho: PW-PB ○ Ho: Pw PB Part (c) In words, state what your random variable P'w-P'B represents. P'w-P'B represents the average difference of white and black female suicide victims, aged 15 to 24. ○ P'w-P'B represents the average difference in proportions of white and black female suicide victims, aged 15 to 24. ○ P'w - P'B represents the difference in the average amount of white and black female suicide victims, aged 15 to 24. O P'W-P'B represents the difference in proportions of white and black female suicide victims, aged 15 to 24. Part (d) State the distribution to use for the test. (Round your answers to four decimal places.) P'w-P'B Part (e) What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.) --Select-- = Part (f) What is the p-value? (Round your answer to four decimal places.) Explain what the p-value means for this problem. ○ If Ho is true, then there is a chance equal to the p-value that the difference between the proportion of 15 to 24 year old white female suicide victims and the proportion of 15 to 24 year old black female suicide victims is at least 0.6%. ○ If Ho is true, then there is a chance equal to the p-value that the difference between the proportion of 15 to 24 year old white female suicide victims and the proportion of 15 to 24 year old black female suicide victims is at most 0.6%. If Ho is false, then there is a chance equal to the p-value that the difference between the proportion of 15 to 24 year old white female suicide victims and the proportion of 15 to 24 year old black female suicide victims is at least 0.6%. ○ If Ho is false, then there is a chance equal to the p-value that the difference between the proportion of 15 to 24 year old white female suicide victims and the proportion of 15 to 24 year old black female suicide victims is at most 0.6%. Part (g) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value. 1/2(p-value) 1/2(p-value) P'w - P'B 1/2(p-value) p-value p-value P'w - P'B 1/2(p-value) Part (h) Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion. (i) Alpha (Enter an exact number as an integer, fraction, or decimal.) απ (ii) Decision: O reject the null hypothesis. O do not reject the null hypothesis P'w P'B P'w - P'B (iii) Reason for decision: ○ Since p-value > a, we do not reject the null hypothesis. O Since p-value a, we reject the null hypothesis. ○ Since p-value