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Sagot :
1.The following is the 90% confidence interval for the mean difference between the park's tree heights in 2009 and 2019:
(11.59, 14.21)
2. The conditions for the confidence interval are of:
A. Large samples and no extreme outliers.
D. Independently sampled pairs.
Given,
What is a confidence interval for the t-distribution?
When the population's standard deviation is unknown, the t-distribution is utilized, and the boundaries of the confidence interval are provided using the following formula:
x ± t s/√n
When the equation's variables are laid down as follows:
The sample mean = x
The critical value = t
The sample size = n
The standard deviation for the sample = s
Using a t-distribution calculator, the critical value is t = 1.6766 for a two-tailed 90% confidence interval with 50 - 1 = 49 df.
The remaining parameters are given as follows:
x = 12.9, s = 5.52, n = 50
Then the lower bound of the interval is of:
12.9 - 1.6766 x 5.52/sqrt(50) = 11.59.
The upper bound of the interval is of:
12.9 + 1.6766 x 5.52/sqrt(50) = 14.21.
Learn more about confidence interval here;
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Question is incomplete. Completed question is given below;
Forest rangers wanted to better understand the rate of growth for younger trees in the park. They took measurements of a random sample of 50 young trees in 2009 and again measured those same trees in 2019. The data below summarize their measurements, where the heights are in feet.
Year Mean SD n
2009 11.4 3.6 50
2019 24.3 8.8 50
Difference 12.9 5.52 50
Round all calculated values to 4 decimal places as appropriate.
1. Construct a 90 confidence interval for the mean difference between the height of trees in the park in 2009 and in 2019.
2. What conditions must be met if we want to perform a hypothesis test and answer the question of the management? Select all that apply:
A. Large samples and no extreme outliers.
B. There must be at least 3 levels of the categorical variable.
C. np^≥10 and n(1−p^)≥10
D. Independently sampled pairs.
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