A big debate in the United States is over whether or not schools should provide

Question

A big debate in the United States is over whether or not schools should provide bilingual (Spanish & English) education for children of immigrants in the United States. Studies such as that by Branum-Martin and colleagues (2010) have investigate this issue by looking at the eventual English-language reading skills of students in bilingual education programs as compared to traditional (English-only) classroom settings**. Consider the following experiment, which is similar to theirs. Results from a wide range of traditional (English-only) classrooms in border states (e.g., Texas, Arizona, California) show that average performance by 1st graders on a standardized test of English reading comprehension is = 128 with a standard deviation of = 31. A sample of n = 136 1st graders in border schools with bilingual education programs is selected and the average English-language reading comprehension of the selected students is found to be M = 135. Based on this data, do bilingual education programs improve English-language reading comprehension? Conduct the appropriate one-tailed hypothesis test at = .01.

**Branum-Martin, L., et al., (2010). Contextual Effects of Bilingual Programs on Beginning Reading. Journal of educational psychology, 102(2), 341-355.

a. What are the appropriate null and alternative hypotheses?

b. What Z score(s) identify the appropriate critical regions?

c. What is the obtained score?

d. What is the appropriate interpretation of your results?

Explanation / Answer

Set Up Hypothesis
Null Hypothesis H0: U<128
Alternate Hypothesis H1: U>128
Test Statistic
Population Mean(U)=128
Given That X(Mean)=135
Standard Deviation(S.D)=31
Number (n)=136
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=135-128/(31/Sqrt(136)
Zo =2.6333
| Zo | =2.6333
Critical Value
The Value of |Z | at LOS 0.01% is 2.33
We got |Zo| =2.6333 & | Z | =2.33
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value : Right Tail - Ha : ( P > 2.6333 ) = 0.0042
Hence Value of P0.01 > 0.0042, Here we Reject Ho

we have evidence to support
bilingual education programs improve English-language reading comprehension

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