Answer the following questions when n= 34 (total number) Student Learning Outcom

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Answer the following questions when n= 34 (total number) Student Learning Outcomes The student will calculate the 90% confidence interval the proportion of students in this school who were bom in · this state · The student will interpret corad ence intervals. · The student will determine the effects of changing conditions on the confidence interval. Collect the Data 1. Survey the students in your dass, asking them if they were born in this state Let X-the number that were born in this state 2. In words, define the random variable P 3. State the estimated distributi on to use. htt /cnx.org/content/col11562/latest Find the Confidence Interval and Error Bound 1. Calcul ate the con fidence interval andthe error bound a. Confidence Interval: b. Error Bound: 2. How much area is in both tails (combined)? 3. How much area isin each tall? = 4. Fill in the blanks on the graph with the areain each section. Then, fill in the number line with the upper and lower limits of the confidence interval and the sample proportion. Figure 8.7

Explanation / Answer

TRADITIONAL METHOD
given that,
possibile chances (x)=14
sample size(n)=34
success rate ( p )= x/n = 0.4118
I.
sample proportion = 0.4118
standard error = Sqrt ( (0.4118*0.5882) /34) )
= 0.0844
II.
margin of error = Z a/2 * (stanadard error)
where,
Za/2 = Z-table value
level of significance, = 0.1
from standard normal table, two tailed z /2 =1.645
margin of error = 1.645 * 0.0844
= 0.1388
III.
CI = [ p ± margin of error ]
confidence interval = [0.4118 ± 0.1388]
= [ 0.2729 , 0.5506]
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DIRECT METHOD
given that,
possibile chances (x)=14
sample size(n)=34
success rate ( p )= x/n = 0.4118
CI = confidence interval
confidence interval = [ 0.4118 ± 1.645 * Sqrt ( (0.4118*0.5882) /34) ) ]
= [0.4118 - 1.645 * Sqrt ( (0.4118*0.5882) /34) , 0.4118 + 1.645 * Sqrt ( (0.4118*0.5882) /34) ]
= [0.2729 , 0.5506]
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interpretations:
1. We are 90% sure that the interval [ 0.2729 , 0.5506] contains the true population proportion
2. If a large number of samples are collected, and a confidence interval is created
for each sample, 90% of these intervals will contains the true population proportion

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