Question 1

Verifying Requirements.In the largest clinical trial ever conducted, 401,974 children were randomly assigned to two groups. The treatment group consisted of 201,229 children given the Salk vaccine for polio, and the other 200,745 children were given a placebo. Among those in the treatment group, 33 developed polio, and among those in the placebo group, 115 developed polio. If we want to use the methods of this section to test the claim that the rate of polio is less for children given the Salk vaccine, are the requirements for ahypothesis test for two proportionssatisfied? Explain why or why not.

Question 2

Notation.In the largest clinical trial ever conducted, 401,974 children were randomly assigned to two groups. The treatment group consisted of 201,229 children given the Salk vaccine for polio, and the other 200,745 children were given a placebo. Among those in the treatment group, 33 developed polio, and among those in the placebo group, 115 developed polio.Consider the Salk vaccine treatment group to be the first sample.Identify the values of n₁, x_1,1, ₁, ₂, x₂, ₂and₂.

n₁is equal to [ Select ] ["201,229", "401,974", "200,745"]

x₁is equal to [ Select ] ["115", "33", "201,229"]

₁is equal to [ Select ] ["1.639", "0.0001639", "6097.8484"]

₁is equal to [ Select ] ["0.9994", "0.9998"]

n₂is equal to [ Select ] ["115", "201,229", "200,745"]

x₂is equal to [ Select ] ["401,974", "115", "33"]

₂is equal to [ Select ] ["0.000572866", "1745.608", "5.72866"]

₂is equal to [ Select ] ["0.9998", "0.9994"]

Calculate the pooled sample proportion using the formulas below: P = X1 + x2 = ??? And q = 1 -p = ??? nit n2- First verify that the two necessary requirements are satisfied. - Identify the null & alternative hypothesis. - Calculate the sample proportion of people who developed dementia in treatment group as: - Calculate the sample proportion of people who developed dementia in placebo group as: P2 = 2 - Calculate the pooled sample estimate p as: p = ni+ 82 - Once you solve for p, solve for q =1 - p - Because we assume in the null hypothesis that py = pr, the value of py - pris 0 in the following calculation of the test statistics Z = (P - P.)-(P - P. ) pq pq - With the test being left-tailed, the critical value is z = ? - Is the P-value greater or less than the significance level of 0.01? Do we reject or fail to reject the null hypothesis?- Since this is a one sided test, if level of significance, a = 0. 01, then confidence level we should use: (1 - 2a)x 100% = - With the above calculated confidence level, Zan = - Calculate the value of margin of error E as shown below. P292 E = Za/2 + n2 - The confidence interval is evaluated as follows, with the confidence interval limits rounded to four significant digits: (P1 - P2) - E My Progress - University X + X C O File | C:/Users/joanna/Downloads/Hypothesis%20Testing%20in%205%20Steps.pdf O E Hypothesis Testing in 5 Steps.pdf 1 / 3 75% + Hypothesis Testing in 5 Steps For all questions throughout the semester that ask you to complete a hypothesis test, please use this outline. It is adaptable to difference situations that ask you to complete a hypothesis test. Step #1: State the hypotheses Sometimes it is helpful to write out the hypothesis in words first then in symbolic form. Always include the symbolic form Be sure you have the correct symbols. Is the test about the population mean? Population standard deviation? Population proportion? Choosing the correct symbol is important. (Notice the word population in all of these: Hypothesis testing is based on population values. Never use sample statistic symbols here, only population symbols For the null hypothesis, there is only one option: (based on equality) Ho:6 = For the alternative hypothesis, there are three options based on the problem H1:6> H1:6 My Progress - University X + X C O File | C:/Users/joanna/Downloads/Hypothesis%20Testing%20in%205%20Steps.pdf E Hypothesis Testing in 5 Steps.pdf 1 / 3 75% + Step #5: Conclusions The first part of the conclusion is the statistical conclusion: Reject or fail to reject H, and why. Keep in mind, reject or fail to reject are the only options. We have not proven H, is true using these steps so we should not accept it. The second part of the conclusion is stating a conclusion in laymen's terms. It amounts to answer the question that is asked in the problem. See my example below. Note that the information in italics are my notes to you. These do not need to be included. Ex: In an interview with Dr. Jones at University of Utah, Dr. Jones mentions that it takes a person on average about 30 minutes to fall asleep*. Suppose a random sample of 40 college students had a mean time to fall asleep of 28 minutes 2 with a known population standard deviation of 6 minutes. Does this sample suggest that college students may fall asleep faster than the suggested 30 minutes? Be sure to include all 5 steps from the hypothesis test https://healthcare.utah.edu/the-scope/shows.php?shows=0_xa3qjafl Note that the information in italics are my notes to you. These do not need to be included with any submissions. Please do not copy and paste such that my notes are included. 1.) State the hypotheses: Ho:u = 30 (null hypothesis, always based on equality. use = sign) H1: u My Progress - University X + X C O File | C:/Users/joanna/Downloads/Hypothesis%20Testing%20in%205%20Steps.pdf E Hypothesis Testing in 5 Steps.pdf 2 / 3 1 - 75% + Ex: In an interview with Dr. Jones at University of Utah, Dr. Jones mentions that it takes a person on average about 30 minutes to fall asleep*. Suppose a random sample of 40 college students had a mean time to fall asleep of 28 minutes with a known population standard deviation of 6 minutes. Does this sample suggest that college students may fall asleep faster than the suggested 30 minutes? Be sure to include all 5 steps from the hypothesis test "https://healthcare.utah.edu/the-scope/shows.php?shows=0_xa3qjafl Note that the information in italics are my notes to you. These do not need to be included with any submissions. Please do not copy and paste such that my notes are included. 1.) State the hypotheses: Ho: u = 30 (null hypothesis, always based on equality.use = sign) H1: u My Progress - University X + X C O File | C:/Users/joanna/Downloads/Hypothesis%20Testing%20in%205%20Steps.pdf O E Hypothesis Testing in 5 Steps.pdf 2 / 3 | - 75% + 4.) Calculations: a.) 1st, the test statistic: (This is always based on the statistic chosen in step 2) Z = 28 - 30 -= -2.108 6/40 b.) 2nd, we can calculate the p-value. (Here, you have the option of either the p-value or a critical value. In this case, I used the p-value. Keep in mind, your conclusion will be the same either way.) P - value = P(Z My Progress - University X + X C O File | C:/Users/joanna/Downloads/Hypothesis%20Testing%20in%205%20Steps.pdf O Hypothesis Testing in 5 Steps.pdf 3 / 3 | - 75% + c.) Draw a picture to help visualize: (In this picture, I drew lines to indicate the rejection region based on our alpha value and then darkened the p-value. As our p-value is inside the rejection region, we are going to reject in the conclusion. The picture helps me draw the conclusions.) 20 0.05 rejecthanregion 0.0175 furto reject - 2.108 5.) Conclusions: a. Since the p-value = 0.0175 H1:8 0.50 (alternative is directional. Notice the symbol for the population mean) In words: (This is optional but can be helpful) H.: The population proportion of babies that are boys is 50%% H1: The population proportion of babies that are boys is greater than 50% 2.) Choose a test statistic in this example, we are dealing with a single sample and testing the sample proportion. We can use a Z-Statistic. As the value for alpha is stated in the problem, we use a = 0.01 with a = 0.01 P(1 - P) 3.) State the assumptions First, we need to assume the sample is a random sample so that it represents the population well. In this problem, this information is not stated so we need to state it here. We are assuming the sample is a simple random sample as it is not stated in the problem. . Second, we need to check to see if the requirements for a binomial distribution are met. In this example, there are 291 independent trials with only 2 possible outcomes. The probability remains constant from trial to trail. Therefoe, the requirements for a binomial distribution are met . Third, we need to test the sample size. In this case, testing that np 2 5 and nq 2 5 291(0.82) = 293 2 5 2 291(0.18) = 52 2 5 Therefore, this requirement is met. 4.) Calculations a.) 1st, the test statistic: (This is always based on the statistic chosen in step 2) 2 - 0.82 - 0.50 = 10.96 0.50 - 0.50 291 b.) 2nd, we can calculate the p-value. (Here, you have the option of either the p-value or a critical value. In this case, I used the p-value. Keep in mind, your conclusion will be the same either way.) Hypothesis Testing.pdf Hypothesis Testing..pdf ~ D Cliff Edge Image Ph.gif Show all X Type here to search 14% 5:57 PM 10/31/2022C My Overvie X UB Quiz: Lab A X Hypothesis X UB Topic: New X K! Kahoot! X A Homework X *Course Her X My Progres X + X C O File | C:/Users/joanna/Downloads/Hypothesis%20Testing%20for%20Proportions%20in%205%20Steps.pdf E Hypothesis Testing for Proportions in 5 Steps.pdf 2 / 3 50% + With a = 0.01 P(1 - P) 3.) State the assumptions First, we need to assume the sample is a random sample so that it represents the population well. In this problem, this information is not stated so we need to state it here. We are assuming the sample is a simple random sample as it is not stated in the problem. . Second, we need to check to see if the requirements for a binomial distribution are met. In this example, there are 291 independent trials with only 2 possible outcomes. The probability remains constant from trial to trail. Therefoe, the requirements for a binomial distribution are met Third, we need to test the sample size. In this case, testing that np 2 5 and nq 2 5 291(0.82) = 293 2 5 291(0.18) = 52 2 5 Therefore, this requirement is met. 4.) Calculations: a.) 1st, the test statistic: (This is always based on the statistic chosen in step 2) 2 0.82 - 0.50 10.96 9.50 . 0.50 291 b.) 2nd, we can calculate the p-value. (Here, you have the option of either the p-value or a critical value. In this case, I used the p-value. Keep in mind, your conclusion will be the same either way. P - value = P(Z > 10.96)