A species of tree under regular conditions grows to an average height of 40-cm in 4 months. You are working with an experimental fertilizer, and you wish to test the claim that the trees grow taller in the same amount of time with this fertilizer. You collect data on 16 saplings, and they have an average height of 40.3-cm with a standard deviation of 5.1-cm. Find the 98% confidence interval for the average height of the saplings with the new fertilizer. (1a) What is the estimate of the standard error of the mean rounded to 3 decimals? SE = (1b) What is the margin of error rounded to 3 decimals? ME = (1c) What is the critical value (the uppermost t-score with 98% in the middle of the distribution) rounded to 3 decimals? tc= Hint for 1c: Use the formula for margin of error to reverse engineer the t-score using the known standard error of the mean and the known margin of error that you provided in parts 1a and 1b. (1d)Calculate the Confidence Interval What is the 98% confidence interval for the average height (in cm) of the samplings with the new fertilizer? Enter answer as an interval such as ( , ) and round values to 1 decimal place.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Note: Please answer all parts of this question(a,b,c,d)
1) A species of tree under regular conditions grows to an average height of 40-cm in 4 months. You are working with an experimental fertilizer, and you wish to test the claim that the trees grow taller in the same amount of time with this fertilizer. You collect data on 16 saplings, and they have an average height of 40.3-cm with a standard deviation of 5.1-cm. Find the 98% confidence interval for the average height of the saplings with the new fertilizer.
(1a) What is the estimate of the standard error of the mean rounded to 3 decimals?
SE =
(1b) What is the margin of error rounded to 3 decimals?
ME =
(1c) What is the critical value (the uppermost t-score with 98% in the middle of the distribution) rounded to 3 decimals?
tc=
Hint for 1c: Use the formula for margin of error to reverse engineer the t-score using the known standard error of the mean and the known margin of error that you provided in parts 1a and 1b.
(1d)Calculate the Confidence Interval
What is the 98% confidence interval for the average height (in cm) of the samplings with the new fertilizer? Enter answer as an interval such as ( , ) and round values to 1 decimal place.
_____________________
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
