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Records show that students score an average of 850 points on an achievement test. A test prep company believe their students will have different scores. To test this hypothesis, they sample 1000 students and find a sample mean of 856 points. They perform the hypothesis test at a confidence level of 95%. a. State the null and alternative hypothesis mathematically b. What is the significance level? c. If 856 is a significantly significant score after being transformed into a z statistic, where will it lie in the distribution below? In area 1, area 2 or area 3?

Records show that students score an average of 850 points on an achievement test. A test prep company believe their students will have different scores. To test this hypothesis, they sample 1000 students and find a sample mean of 856 points. They perform the hypothesis test at a confidence level of 95%. a. State the null and alternative hypothesis mathematically b. What is the significance level? c. If 856 is a significantly significant score after being transformed into a z statistic, where will it lie in the distribution below? In area 1, area 2 or area 3?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Records show that students score an average of 850 points on an achievement test. A test
prep company believe their students will have different scores. To test this hypothesis, they
sample 1000 students and find a sample mean of 856 points. They perform the hypothesis test
at a confidence level of 95%.
a. State the null and alternative hypothesis mathematically
b. What is the significance level?
c. If 856 is a significantly significant score after being transformed into a z statistic, where will
it lie in the distribution below? In area 1, area 2 or area 3?

The image features a standard normal distribution curve, often referred to as a bell curve, which is symmetrical in shape. This type of curve is used in statistics to represent the distribution of values, scores, or measurements. ### Breakdown of the Curve: - **Center of the Curve (Area 2):** - Encompasses 95% of the data within the distribution. - This central area represents the mean (average) with standard deviations typically ranging from -2 to +2. - **Tails of the Curve (Area 1 and Area 3):** - Each tail (Area 1 on the right and Area 3 on the left) represents 2.5% of the distribution. - This means that each tail contains the extreme values on either side of the mean. - Often used to identify outliers or rare events in a dataset. ### Usage in Statistics: The curve is utilized in various statistical analyses, including hypothesis testing and confidence interval estimation. The 95% area indicates a common confidence level used to assess the certainty or reliability of the statistical conclusions.
Transcribed Image Text:The image features a standard normal distribution curve, often referred to as a bell curve, which is symmetrical in shape. This type of curve is used in statistics to represent the distribution of values, scores, or measurements. ### Breakdown of the Curve: - **Center of the Curve (Area 2):** - Encompasses 95% of the data within the distribution. - This central area represents the mean (average) with standard deviations typically ranging from -2 to +2. - **Tails of the Curve (Area 1 and Area 3):** - Each tail (Area 1 on the right and Area 3 on the left) represents 2.5% of the distribution. - This means that each tail contains the extreme values on either side of the mean. - Often used to identify outliers or rare events in a dataset. ### Usage in Statistics: The curve is utilized in various statistical analyses, including hypothesis testing and confidence interval estimation. The 95% area indicates a common confidence level used to assess the certainty or reliability of the statistical conclusions.
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