do students who learned English as well as another language simultaneously score worse on the SAT critical reading exam than the general population of test takers? the mean score di 501. A random sample of 100 test takers who learned English as another language simultaneously has a mean of reading score of 485 with a standard deviation of 116 do these results suggest that students who learn English as well as another language
Z = (mean1 - mean2)/standard error (SE) of difference between means
SEdiff = √(SEmean1^2 + SEmean2^2)
SEm = SD/√n
If only one SD is provided, you can use just that to determine SEdiff.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.
so, for the fist part it will be
(501-485)/116= .1379? what is the SE?
To determine whether students who learn English as well as another language simultaneously score worse on the SAT critical reading exam than the general population, we can conduct a hypothesis test.
Hypotheses:
- Null hypothesis (H₀): There is no significant difference between the mean score of students who learn English as well as another language and the mean score of the general population.
- Alternative hypothesis (H₁): Students who learn English as well as another language score significantly worse on the SAT critical reading exam than the general population.
Next, we need to calculate the test statistic, which in this case is the z-score. The formula for calculating the z-score is:
z = (sample mean - population mean) / (population standard deviation / √sample size)
Given data:
- Mean score of the general population (μ): 501
- Sample size (n): 100
- Sample mean (x̄): 485
- Sample standard deviation (σ): 116
Calculating the z-score:
z = (485 - 501) / (116 / √100)
z = -16 / (116 / 10)
z = -1.379
The next step is to compare the calculated z-score with the critical value at a chosen significance level (typically denoted as α). Assuming a significance level of 0.05 (or 5%), we can look up the critical value using a standard normal distribution table or a statistical calculator. For a two-tailed test, the critical values are -1.96 and 1.96.
Since the calculated z-score (-1.379) is within the range of -1.96 to 1.96, we fail to reject the null hypothesis. This means that there is no significant evidence to conclude that students who learn English as well as another language simultaneously score worse on the SAT critical reading exam compared to the general population.
Please note that this analysis is based on the assumption that the data follows a normal distribution and that the sample is representative. Additionally, it is always good practice to consider other factors and conduct further analysis if required.