Do Z-Tests Determine Proportion of Students with Grades <50 and >80?

  • Thread starter aptiva
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In summary, to calculate the proportion of students in each population that would receive a grade <50 and >80, you would perform a Z-test using the given M and SD values and look up the corresponding P values in a Z table. Then, subtract the P value from 0.5 to get the proportion.
  • #1
aptiva
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Hi all:

Homework Statement



Sample 1: M = 62.77, SD = 6.52
Sample 2: M = 72.91, SD = 6.22
Sample 3: M = 74.61, SD = 6.60

Homework Equations



Now if I wanted to calculate what proportion of students in each population would be expected to receive a grade <50 and receive a grade >80, would I perform a Z-test using Z = (X-mu)/Sd


The Attempt at a Solution



For example, in sample 1:

(For <50)
Z = 50 - 62.77 / 6.52 = -1.959, P = 0.0202 (according to Z-table)
So, .5 - .0202 = .4798 = approximately 48% of the students in the first population would receive a score <50...is that correct?

(For >80)
Z = 80 - 62.77 / 6.52 = 2.65, P = 0.4965(according to Z-table)
So, .5 - .4965 = .0035 = approximately .35% of the students in the first population would receive a score >80...?
 
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  • #2
Thank you!Yes, this is correct. To answer your question, you would need to perform a Z-test using Z = (X-mu)/Sd for each population. For the <50 calculation, you would use 50 for X and for the >80 calculation, you would use 80 for X. Then, you would look up the corresponding P values in a Z table. Lastly, you would subtract the P value from 0.5 to get the proportion of students that are expected to receive a grade <50 or a grade >80.
 

1. What is a Z-test?

A Z-test is a statistical test used to determine whether two population means are different when the variances are known and the sample size is large enough. It is commonly used to compare a sample mean to a known population mean.

2. When should I use a Z-test?

A Z-test should be used when the sample size is greater than 30, the population standard deviation is known, and the data is normally distributed. It is also appropriate when comparing a sample mean to a known population mean.

3. How do I perform a Z-test?

To perform a Z-test, you will need to calculate the Z-score, which is the difference between the sample mean and the population mean divided by the standard deviation. Then, you can use a Z-table or statistical software to find the p-value and determine the significance of the results.

4. What is the difference between a Z-test and a T-test?

The main difference between a Z-test and a T-test is the assumptions about the population. A Z-test assumes that the population standard deviation is known, while a T-test assumes that it is unknown. Additionally, a Z-test is used for large sample sizes, while a T-test is used for smaller sample sizes.

5. Can a Z-test be used for non-numerical data?

No, a Z-test is typically used for numerical data where the sample mean can be calculated. For non-numerical data, other statistical tests such as the chi-square test or Fisher's exact test should be used.

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