Statistics of Ear Infections in Elementary School
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Many elementary school students in a school district currently have ear infections. A random sample of children in two different schools found that 16 of 42 at one school and 21 of 36 at the other had this infection. At the .05 level of significance, is there sufficient evidence to conclude that a difference exists between the proportion of students who have ear infections at one school and the other?
a. No, there is not sufficient information to reject the hypothesis that the proportions of students at the two schools who have ear infections are the same because the test value -1.78 is inside the acceptance region (-1.96,1.96).
b. Yes, there is sufficient information to reject the hypothesis that the proportions of students at the two schools who have ear infections are the same because the test value -2.34 is outside the acceptance region (-1.96,1.96).
c. Yes, there is sufficient information to reject the hypothesis that the proportions of students at the two schools who have ear infections are the same because the test value -8.76 is outside the acceptance region (-1.96,1.96).
d. Yes, there is sufficient information to reject the hypothesis that the proportions of students at the two schools who have ear infections are the same because the test value -15.73 is outside the acceptance region (-1.96,1.96).
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Solution Summary
The solution examines ear infections in elementary school. A 0.05 level of significance is used.
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The correct answer is a) No, there is not sufficient information to reject the hypothesis that the proportions of students at the two ...
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- BSc , Wuhan Univ. China
- MA, Shandong Univ.
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- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
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