Question

Page 8 4. In a Gallup poll done in May, 2020 ( http://news.gallup.com/poll/312929/record-low-say-death-penalty-morally- acceptable.aspx), a random sample of 1,028 U.S. adults were surveyed and 54% said that the death penalty was "morally acceptable." (a) Compute a 99% confidence interval for the proportion of U.S. adults that believe the death penalty is "morally acceptable." [5 pts] (b) Test at the 5% significance level if the proportion of U.S. adults that believe the death penalty is "morally acceptable" is more than 50%. 1. Define the parameter(s) and state the hypotheses: (3 pts) ii. Find the observed sample statistic (using your calculator) and the test statistic (using a formula). Use proper notation for the sample statistic ( X or ), and clearly identify your test statistic as either a 2-score or a t-score. [4pt]

We do not use critical values at all in our course so please avoid using them when giving me explanations, as they can cause confusion on my end between your explanation and what im learning on my course

here is the link in the page https://news.gallup.com/poll/312929/record-low-say-death-penalty-morally-acceptable.aspx though the data is already provided in the problem so i dont think its needed to solve. i give you the link in case you want to go over it, if you do go over it let me know how and what information you took from it that helped

Answer 1

4. a)

b)

Let p denotes the population proportion. Let p denotes the sample proportion and n denotes the sample size. Here, Ô = 0.540, n = 1028, standard error = 0.540 * (1 – 0.540) 1028 = 0.015545 0.0155 At 99 percent confidence level, Margin of error is *(1 - ē ME * 21-0.99 2 0.540 * (1 – 0.540) 1028 * 20.005 = 0.540 * (1 – 0.540) *2.575829 = 0.040040 0.040 1028 n a 99 percent confidence interval for the population proportion p is Ô *(1-P) = P + * 21-0.99 2 n = 0.5400 + 0.540 * (1 – 0.540) 1028 * 20.005 = 0.5400 + 0.540 * (1 – 0.540) 1028 * 2.575829 = 0.5400 + 0.040040 = (0.499960,0.580040) ~ (0.500,0.580)

Let p denotes the population proportion. Hypotheses : To test null hypothesis H :P < 0.5 against alternative hypothesis H1 :p> 0.5 Let o denotes the sample proportion and n denotes the sample size. Here, P = 0.5400, n = 1028, po = 0.5, standard error 0.5*(1 -0.5) 1028 0.015595 The test statistic can be written as: Z= Cê po) Po*(1-P) n which under H, follows a standard normal distribution. Decision rule / Rejection region : We reject H, at 0.01 level of significance if P-value < 0.01 or if ZSTAT 20.01 = 2.326348 0.4 0.3- 0.2- 0.1 - 0.0 - -2 Now, Value of test statistic: The value of the test statistic ZSTAT = = 2.564995 ~ 2.565 (0.5400 – 0.5) 0.5*(1-0.5) 1028 The critical value critical = 20.01 = 2.326348 2.326 P - value = P(Z > ZSTAT) = P(Z > 2.564995) = 1- P(Z < 2.564995) =1-0.994841 = 0.005159 0.0052 Conclusion : Since p-value < 0.01 and 2STAT > Zcritical = 2.326348, so we reject H, at 0.01 level of significance Hence, we can conclude that the population proportion is significantly greater than 0.5