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an innovative math project goal was to introduce innovative approaches to teaching mathematics and engage students in group investigations and mathematical modeling. after a field test in 36 high schools over a three-year period researchers compared the performance of students in this new curriculum with those in a traditional curriculum. scores for 320 students in this new curriculum were compared to scores in a control group (traditional program) of 273 students. a 95% confidence interval for the mean difference in scores was calculated to be [5.573, 11.427]. A. State the null and alternative hypothesis that the researchers most likely used to compare the performance between these two types of curriculums.
B. What is the margin of error of this confidence interval?
C. If a 98% confidence interval would have been created, would the margin of error be larger or smaller.
D. Based on the confidence interval can the researchers conclude that there is a difference between the means in performance scores for the two types of math curriculum? Explain how you reached this conclusion.

Sagot :

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The 95% confidence interval for the mean difference of scores [5.573,11.427].

A) Null and Alternative hypothesis are

H₀ : μ₁ - μ₂ =0

Hₐ : μ₁ - μ₂ ≠ 0

B) Margin of Error of 95% confidence interval is 2.927

C) Margin of error increase with increasing the confidence interval. So, the margin of error large at 98% confidence interval.

D) Because zero is not included in the confidence interval, and all values in the confidence interval [5.573, 11.427] are positive.

A sample of scores for 320 students in this new curriculum were compared to scores in a control group (traditional program) of 273 students.

(A) Null and Alternative hypothesis are

H₀ : μ₁ - μ₂ =0 ( There is no difference between the means in performance scores for the two types of math curriculum )

Hₐ : μ₁ - μ₂ ≠ 0 ( There is a difference between the means in performance scores for the two types of math curriculum ) (Claim)

(B)We have given data that ,

Confidence Interval : [5.573, 11.427]

Sample mean (X-bar) is given by:

X-bar =( 5.573 + 11.427)/2 =17/2 = 8.5

Using margin of error formula,

MOE = mean - lower bound of confidence interval

Margin of Error = 8.5 - 5.573= 2.927

=> Margin of Error = 2.927

(C)If a 98% confidence interval would have been created, the margin of error would be larger because the margin of error increases as the confidence level increases from 95% to 98%

(D)Based on the confidence interval the researchers can conclude that there is a difference between the means in performance scores for the two types of math curriculum because 0 is not included in the confidence interval, [5.573, 11.427] and all values in the confidence interval [5.573, 11.427] are positive.

To learn more about Confidence interval, refer:

https://brainly.com/question/17212516

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