Determine the sample size required to estimate the mean score on a standardized test within 4 points of the true mean with 98% confidence. Assume that s = 14 based on earlier studies.

Sample size required to estimate the mean score on a standardized test  is 67.

The confidence level (C) = 98% = 0.98

α = 1 - C = 0.02

α/2 = 0.02/2 = 0.01

The z score of α/2 is the same as the z score of 0.49 (0.50 - 0.01) which is equal to 2.33

Given that:

Standard deviation (σ) = 14, margin of error (E) = 4, n = sample size, hence:

Hence the sample size required to estimate the mean score on a standardized test  is 67.

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67

Step-by-step explanation:

Formula to calculate sample size: , where s = standard deviation on prior studies , z* = two tailed critical value for confidence level , E = margin of error

Given: E = 4 , s= 14 and confidence level = 98%

Z-value for  98% confidence = 2.326

Then, required sample size:

Hence, the required sample size = 67 .

Hello,

The rate of change is the slope (rise/run, y/x). To find that, we use the equation (y2-y1) over (x2-x1). It means take the second "y" and subtract it from the first "y" and the same to "x". If I plug in the numbers, it would be (3-6) over (5-4), and after you subtract, the answer simplifies to: -3/ 1 which is -3. Yay! We got the slope (rate of change) done.

Now let's find the y-intercept by using the formula of point-slope form, 
y-y1= m (slope) (x-x1). This is saying you "y" is subtracted from the first 
"y" of the points which equals the slope (m) times the quantity of "x" subtracted by the first "x" of the points. 

Let's plug the numbers in: y-6 = -3 (x-4). Let's distribute -3 to the parenthesis, and after that it should simplify to: y-6 = -3x + 12. To get "y" by itself, add 6 to both sides: y = -3x +18. We have finally found the slope-intercept equation for those two points (4,6) and (5,3). To then find the y-intercept in this equation, it would be the 18, because -3 is the slope, so that makes 18 the y-intercept.

In conclusion, the rate of change is -3 and the y-intercept is 18. 

I hope this helps!

May