Assume that last year in a particular state with 700000 children there were 1214 children out of 30900 in a random sample who were diagnosed with Autism Spectrum Disorder. Nationally, 1 out of 88 children are diagnosed with ASD. Is there sufficient data to show that the incident rate of ASD is higher in that state than nationally? Test at the 2% level.P: PARAMETER What is the correct parameter symbol for this problem? Correct What is the wording of the parameter in the context of this problem? CorrectH: HYPOTHESES Fill in the correct null and alternative hypotheses: The value of p on this one is a fraction....leave it exact. 𝐻0: Correct Correct 188Correct 𝐻𝐴: Correct Correct 188Correct A: ASSUMPTIONS Since Correct information was collected from each object, what conditions do we need to check? Check all that apply. 𝑁≥20𝑛𝑛(1-𝑝̂)≥10σσ is known.σσ is unknown.𝑛≥30 or normal population.𝑛(1-𝑝)≥10𝑛𝑝≥10𝑛(𝑝̂)≥10Partially correct Check those assumptions: Round computations to 2 decimal places. 1. 𝑛𝑝 = 30900Incorrect which is Correct 10Correct 2. 𝑛(1-𝑝) = 30900Incorrect which is Correct 10Correct 3. 𝑁 = 1000000Incorrect which is Correct 30Incorrect If no N is given in the problem, use 1000000N: NAME THE PROCEDURE The conditions are met to use a .T: TEST STATISTIC The symbol and value of the random variable on this problem are as follows: Leave this answer as a fraction. = The formula set up of the test statistic is as follows.: (Leave any values that were given as fractions as fractions) 𝑧=𝑝̂-𝑝𝑝(1-𝑝)𝑛=( - )/(( ⋅(1- )) / ) Final answer for the test statistic from technology. Round to 2 decimal places: z = O: OBTAIN THE P-VALUE Report to 4 decimal places. It is possible when rounded that a p-value is 0.0000 P-value = M: MAKE A DECISION Since the p-value , we .S: STATE A CONCLUSION There significant evidence to conclude
Question
Assume that last year in a particular state with 700000 children there were 1214 children out of 30900 in a random sample who were diagnosed with Autism Spectrum Disorder. Nationally, 1 out of 88 children are diagnosed with ASD. Is there sufficient data to show that the incident rate of ASD is higher in that state than nationally? Test at the 2% level.P: PARAMETER What is the correct parameter symbol for this problem? Correct What is the wording of the parameter in the context of this problem? CorrectH: HYPOTHESES Fill in the correct null and alternative hypotheses: The value of p on this one is a fraction....leave it exact. 𝐻0: Correct Correct 188Correct 𝐻𝐴: Correct Correct 188Correct A: ASSUMPTIONS Since Correct information was collected from each object, what conditions do we need to check? Check all that apply. 𝑁≥20𝑛𝑛(1-𝑝̂)≥10σσ is known.σσ is unknown.𝑛≥30 or normal population.𝑛(1-𝑝)≥10𝑛𝑝≥10𝑛(𝑝̂)≥10Partially correct Check those assumptions: Round computations to 2 decimal places. 1. 𝑛𝑝 = 30900Incorrect which is Correct 10Correct 2. 𝑛(1-𝑝) = 30900Incorrect which is Correct 10Correct 3. 𝑁 = 1000000Incorrect which is Correct 30Incorrect If no N is given in the problem, use 1000000N: NAME THE PROCEDURE The conditions are met to use a .T: TEST STATISTIC The symbol and value of the random variable on this problem are as follows: Leave this answer as a fraction. = The formula set up of the test statistic is as follows.: (Leave any values that were given as fractions as fractions) 𝑧=𝑝̂-𝑝𝑝(1-𝑝)𝑛=( - )/(( ⋅(1- )) / ) Final answer for the test statistic from technology. Round to 2 decimal places: z = O: OBTAIN THE P-VALUE Report to 4 decimal places. It is possible when rounded that a p-value is 0.0000 P-value = M: MAKE A DECISION Since the p-value , we .S: STATE A CONCLUSION There significant evidence to conclude
Solution
The question seems to be asking for a step-by-step solution to a hypothesis testing problem related to the incidence rate of Autism Spectrum Disorder (ASD) in a particular state compared to the national rate. Here's how you can approach it:
P: PARAMETER The parameter symbol for this problem is p, which represents the proportion of children diagnosed with ASD in the state.
H: HYPOTHESES The null hypothesis (H0) is that the state's ASD incidence rate is equal to the national rate, i.e., p = 1/88. The alternative hypothesis (HA) is that the state's ASD incidence rate is higher than the national rate, i.e., p > 1/88.
A: ASSUMPTIONS We need to check the following conditions:
- The sample size is large enough (np ≥ 10 and n(1-p) ≥ 10).
- The population size is at least 20 times the sample size (N ≥ 20n).
N: NAME THE PROCEDURE Since we're testing a proportion, we can use a one-sample z-test for proportions.
T: TEST STATISTIC The test statistic is calculated using the formula: z = (p̂ - p) / sqrt[(p(1 - p) / n] where p̂ is the sample proportion, p is the population proportion, and n is the sample size.
O: OBTAIN THE P-VALUE The p-value is obtained by comparing the calculated z-score with the standard normal distribution. The p-value represents the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true.
M: MAKE A DECISION If the p-value is less than the significance level (0.02 in this case), we reject the null hypothesis.
S: STATE A CONCLUSION If we reject the null hypothesis, we can conclude that there is significant evidence to suggest that the incidence rate of ASD in the state is higher than the national rate. If we fail to reject the null hypothesis, we conclude that there is not enough evidence to suggest a higher incidence rate in the state.
Similar Questions
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