Confidence Intervals for Precipitation and Extreme Temperatures

This assignment provides a detailed analysis of precipitation and extreme temperature data using confidence intervals. The solution calculates the proportion of months with no days of significant precipitation and constructs a 95% confidence interval for this proportion. Additionally, it calculates a 99% confidence interval for extreme maximum temperatures. The assignment includes the formulas and calculations used to derive the confidence intervals and provides a clear interpretation of the results. This analysis is designed to help students understand how to apply statistical methods to real-world data and interpret the results. The solution provides a step-by-step guide to understanding and solving the assignment.

For your third journal entry, consider again the variable DP05. How many months had no days
with 0.5 inches or more of precipitation? What proportion of months had no days with 0.5 inches
or more of precipitation? Construct a 95% confidence interval for the proportion of months that
had no days with 0.5 inches or more of precipitation. Does this analysis make sense?
Solution
The total sample size is 347. Out of 347, 36 months had no days with 0.5 inches or more of
precipitation
The proportion of months had no days with 0.5 inches or more of precipitation is 0.1037
The 95% confidence interval for the proportion of months that had no days with 0.5 inches or
more of precipitation is calculated by using the formula given below
( p−Z1− α
2
∗
√ p∗( 1− p )
n , p+ Z1− α
2
∗
√ p∗( 1− p )
n )
(0.1037−1.96∗
√ 0.1037∗( 1−0.1037 )
347 , 0.1037+1.96∗
√ 0.1037∗( 1−0.1037 )
347 )
= (0.0717, 0.1358)
Therefore, the 95% confidence interval for the proportion of months that had no days with 0.5
inches or more of precipitation is (0.0717, 0.1358)
Now consider the variable EMXT (extreme maximum temperature). Construct a 99% confidence
interval for the extreme maximum temperature for a month. Does this analysis make sense
The 99% confidence interval for the extreme maximum temperature for a month is calculated by
using the formula given below
(x−
t1− α
2 , (n−1 )∗s
√n , x+
t 1− α
2 , (n−1 )∗s
√n )
The table given below shows the workings of confidence interval of extreme maximum
temperature for the month

Confidence Interval Estimate for the
Mean
Data
Sample Standard
Deviation
91.5754023
8
Sample Mean
219.855907
8
Sample Size 347
Confidence Level 99%
Intermediate Calculations
Standard Error of the
Mean
4.91602517
5
Degrees of Freedom 346
t Value 2.5901
Interval Half Width 12.7331
Confidence Interval
Interval Lower Limit 207.12
Interval Upper Limit 232.59
From the above table, we see that the 99% confidence interval for the extreme maximum
temperature for a month is (207.12, 232.59). This indicates that, when repeated samples are
taken from the same population, then 99 out of 100 times the true mean extreme maximum
temperature for a month will fall within this interval