Answer :
Answer: (97.63, 99.77)
Step-by-step explanation:
Given the data:
99.6 99.7 97.9 98.6 97.7
Using calculator, we can obtain the mean and standard deviation of the sample data:
Mean(m) = 98.7
Standard deviation = 0.93
Sample size (n) = 5
Using the relation to find confidence interval :
Mean ± Zcrit * (s/√n)
Zcrit at 99% = 2.576
98.7 ± 2.576 * (0.93 / √5)
Lower limit : 98.7 - (2.576 * 0.4159086) = 97.6286194464 = 97.63 ( 1 decimal place)
Upper limit : 98.7 + (2.576 * 0.4159086) = 99.7713805536 = 99.77 ( 1 decimal place)
(97.6, 99.8)
Final answer:
A 99% confidence interval for the mean high temperature of these towns is calculated using the sample mean, standard deviation and appropriate t-value. It requires computation of sample mean, standard deviation, standard error and then utilizing these in the formula for the confidence interval.
Explanation:
To create a 99% confidence interval for the mean temperature, we will primarily need two things: the sample mean (μ) and the standard deviation (σ). The sample mean is simply the average of the temperatures you provided, which in this case equals (99.6 + 99.7 + 97.9 + 98.6 + 97.7) / 5 = 98.7 degrees Fahrenheit. The standard deviation can be calculated using the formula for the population standard deviation.
Once we have these, we can use the t distribution to generate our confidence interval, since we know that temperatures are normally distributed and our sample size is relatively small (n<30). For a 99% confidence interval with 4 degrees of freedom (5-1), the t-value roughly equals 3.747, according to the t-distribution table.
The standard error (σ/√n) equals standard deviation divided by the square root of the number of samples. Plugging in the values, we can now compute the confidence interval as follows: μ ± t*(σ/√n).
Learn more about Confidence Interval here:
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