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Answer :
The correct option is option (B).
For the given scenario B) z-score test statistic would be used.
To determine if the University of Idaho students have a significantly higher mean on the SAT verbal test compared to the known population mean, we would use a z-score test statistic, specifically a one-sample z-test.
Here's why the one-sample z-test is the appropriate choice:
1. The population standard deviation is known to us (100), which allows us to use the z-test instead of the t-test. The t-test is typically utilized when the population standard deviation is unknown and must be estimated using the sample standard deviation.
2. We have a single sample of interests (the 50 students from the University of Idaho) and a single population mean to compare this sample against (the known population mean of 500). This points to a one-sample test rather than something like ANOVA or a repeated measures test, which would be used for comparisons involving more than two groups or paired data.
3. The sample size is greater than 30 (n = 50), which suggests that the distribution of sample means is likely to be normally distributed due to the Central Limit Theorem. This justifies using the z-test.
4. Our goal is to determine if there is a significant difference in means, specifically checking if the University of Idaho students score higher than the population mean. This identifies the use of a test statistic that compares a sample mean to a known population mean, again supporting the one-sample z-test.
Given this information, the correct statistical test for this scenario is: B. z-score test statistic
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